All right, I took a few days to write all this down and I would like it to be put in op in spoiler, otherwise it will take too much room. I wrote things which I thought would be useful for new player and ever for old ones. It's a perfect circle monarch guide
Raiza the Storm Monarch - This guy is huge. He is probably the key card of this deck. He was the best monarch at the time (he got limited to 1 and overlapped by Caius next format). He was able to create infamous "Raiza locks" (spinning multiple cards to the opponent's deck and ruining his draw phase). This is something that new players don't understand as being necessary good (the "Why would I waste a card to summon a guy, only to spin a card, and opponent will draw it next turn" logic) but it is the reason this guy was so huge back then. Always run 3 of him.
Zaborg the Thunder Monarch (can be replaced with Thestalos the Firestorm Monarch) - This guy is not as big as Raiza is, but he definitely does his job here. I suggest running him over the Thestalos just because in this environment it's more important to have monster removal than random hand control. In meta full of zombies and other PC monarchs, you just want to get rid of those pesky recruiters and NOT to trigger them (Mystic Tomato, Pyramid Turtle and Giant Rat being the most common).
Cyber Dragon - This card has been a staple since its release in August 2005 and it remained that way up to this point. Nothing much to say, free summon, runs over stuff, instant tribute fodder for Monarchs. Can be a dead draw, so running at 2 this format is just enough.
Breaker the Magical Warrior - After spending six months being forbidden, Breaker is back to one and ready to kick it. Back then, this guy was relevant to the metagame, he was also very dangerous counterplay to "T-set" (set monster set backrow) opening, as he could net you +2 advantage right away. He did not have priority so Bottomless Trap Hole, Book of Moon, Torrential Tribute and PWWB can screw you. Very effective in late game when breaks that Mirror Force that could cost you a game. If you play this guy on the empty field, your opponent my not want to set anything in fear of losing it to Breaker and then you can wreak havoc.
Card Trooper - MVP of the last format. He got limited with the good reason. He mills 3 cards, runs over 80% of relevant mosters and then floats when gets destroyed, thus neting you an instant plus. This bad boy was part of the most notorious troop-dup combo that gives you three 1900 beaters that are unaffected by Mirror Force (you don't want to spend your Mirror Force to make a -1, right?). He is pretty dangerous this format as well, although not having the same OTK potential, he works well with Pot of Avarice, frog and D-heroes. Run him!
Sangan - Little furball is staple monster in every deck since his release in MRD and this time it's no different. Searches more than half of your monster count (not reaching for Monarchs, CyDras, Breaker and Stratos) and there's literary no way to get him NOT to search (DDWL is not played as it used to be) because there's no banishing stuff. Perfect for tributing for Monarch, net you a nice plus. Best use of the furball is to grab that Frog you need. Once again, an absolute staple!
Mystic Tomato - This may look like a strange and slow pick for fast-paced environment but this card is just awesome. Grabs you Sangan, Reaper, Snipe Hunter and all the D-heroes you run. If you play him face-up attack position you may force removal, as your opponent doesn't want you to pull a chain of self replacing monsters ending with something like Snipe Hunter to smash his face very next turn. Can recruit Mali, to be tributed for Monarch, instantly enabling next Mali.
Snipe Hunter - He's limited with a reason. Although luck-based, you have 67% chance to destroy and discarding a card is not a real downside in this deck. This card is highly used in all the decks, and it should be counted on. I suggest you to run him and to carefully play him when the time is right. If you play him on the T-set or on the field that contains backrow and monster(s), I suggest to hit the monster first (when you have priority in summon-response window, goat players should know that well). If you decide to destroy their backrow first, you may hit the chainable and eat a -1 which is not really best use of Snipe Hunter.
Spirit Reaper - Very versatile. This card defined a whole format before finally got limited and it's still very annoying for the aggressor. This card forces opponent to use his removals preemptively and forces targeting effects (like forcing Brain Control only to get a chance to swing directly). Very effective at stalling, easy to bring to the field (searched by Sangan and Tomato). Run him, especially if you run Tomato.
Treeborn Frog - Infinite tribute fodder, infinite attack blocker against one monster. Very effective, yet very feared by everyone. Don't expect it to stay in your graveyard for too long, your opponent will try to banish it with D.D. Crow or Book of Life. (In my case) it's always the HIGHEST PRIORITY target for Sangan search.
Don't set this, because you will cry so hard when this gets NoC-ed (yeah, zombie decks usually run 2 Noblemen).
Destiny Heroes - 2 Malicious, 1 Fear Monger, 1 Disk, 1 Stratos, 2 D-Draw, 1 Rota. This line-up is fine if you ask me. Running 2 mongers will clog your hand and you will probably want to run third D-Draw, which I don't recommend (I used to play this deck with 3 D-Draws and I always drew it when I had no d-heroes, it was cloggy as f and I tweaked it after 2 games or so). Malicious is semi-limited which highly killed card's efficiency but it's still playable. Disk Commander-Fear Monger is still very powerful combo and your opponent will be prepared for it. Getting Disk to the graveyard is very important and it telegraphs your Premat/CotH (your opponent will start to set S/T removal). On of my favourite plays is discarding that Disk and then playing Call of the Haunted on something else, let's say Sangan, to force that removal or D.D. Crow, and then, when the air is clear play Premat and bring Disk. This can be very devastating. Stratos is a +1 when summoned, has nice 1800 ATK body and can be pulled by Rota. I suggest playing Rota right away when you draw it so you can pull that Stratos instead of drawing it (or even worse, running out of Rota targets in deck). Only exception to this is if you're playing Avarice and shuffling that Stratos into deck, then you can play Rota and pull Stratos for another plus.
Best turn 1 play is Rota-->Stratos-->Disk/Mali-->D-Draw (if no D-Draw, it's also useful with PWWB or Vortex). Deciding what to search with Stratos often depends on your current hand. If you're holding premat/call you want Disk in hand and if you're holding Raiza, then go for Mali. Fear monger is searched on very rare occasions, only if it's your only D-Hero left or if you only have him and 1 Mali (Remember, in order to keep your Mali live, you need to have 1 in deck).
One false telegraph play I love: You have 1 Mali and 1 Disk in grave and 1 Mali in hand alongside D-Draw. If you haven't played a monarch yet (which is very frequent thing mostly), your opponent will fear that monarch play and try to prevent it. Now, you can play that D-Draw and discard malicious, but instead you don't. Next turn, your opponent will probably play Book of Life banishing Mali from your graveyard in fear of Monarch play and leave your Disk safe. Then you can play D-Draw discard Mali play you wanted, and safely bringing back Disk.
Brain Control - Another MVP card of Troop Dupe format that got limited. It was very cancerous at 3 and I'm completely fine with it at 1. It used to create notorious OTK's and enabled Monarch easy as f, but not any more. It's staple and it should be used very carefully. Nice play with this card is stealing a monster, tribute for Monarch, spin/destroy one card and then attack directly. This play is +1 right away, but requires your opponent to have 2 cards on the field. Always respect this card and use it very wisely (you can spam it all day like you did in Troop Dupe).
Pot of Avarice - A +1. It's often hard to pull but your recruiters, Snipe and PWWB help you fill your graveyard. Good for fixing dead Maliciouses. It's at 2 and you should run both copies, in case it's a dead card you can always discard it to Snipe, Vortex or PWWB.
Lightning Vortex - You're supposed to play 2 copies but you can go with one as well. It's great agains zombie swarms and against field full of pesky recruiters you don't want to attack into. Discard your discard fodders with this card. If you can enable your frog, Mali or Disk, don't be afraid to play this card preemptively.
Also, don't be afraid to play it as a -1 on opposing Pyramid Turtles.
Heavy Storm - Very skilled card. Keeps everyone's attention and disallows players to "set 4, pass". I think that this card should always be legal as it PUNISHES overextension as f. Use it smartly. One good play (maybe overrated) is "Pro-Storm" (well-known for goat players), setting Heavy and waiting for opponent to set 2 or more, then flipping Heavy. It's quite useful in this format because there's no Stardust Dragon, no Starlight Road, nobody plays Solemn Judgment. Always respect this card and use it wisely, you have only one.
Mystical Space Typhoon - Very skilled card. It was (in my opinion) maybe even better than Heavy Storm, because nobody is stupid enough to set 4 cards and risk Heavy, but everyone sets individual backrow. MST gets rid of continuous/equip/field spell cards, most notably Premature Burial, Call of the Haunted, Card of Safe Return and every stall spell/trap. You can also do well-known "end of turn MST the card you just set" which is awesome if you're planning an aggression next turn. MST is always 1-for-1 trade and I think it would be retarded for this card to be legal at 2 or more this format (or every format until Synchroes came out).
Premature Burial - Another staple since it came out. Works the best with Disk Commander but has other uses. Can bring back Sangan to be tributed for Monarch. Can bring back Monarch or CyDra to be beatstick. You can do whatever you want with it. Opposing player will always try to out it with MST or Dust Tornado (and will probably save those cards for Premat/Call), so be aware of it. Remember, if your opponent chains MST to your Premature (that targeted Sangan) you will NOT search!!!
Scapegoat - I think this card is a bit underrated in any non-goat format. It has potential to prolong your life, to block Spirit reaper attack, to chain to Breaker or Snipe Hunter. I would suggest using this, but if you need to find a room for something else, this card would be your #1 pick for cutting. Remember not to block yourself with tokens when there's no need to.
Mirror Force - Card we all know well. It's been a staple for so many years. Most feared card when it comes to battle phase. Nothing much to say, back then it was true staple and rightfully limited.
Torrential Tribute - Same as Mirror Force, it's staple for years and was limited for a reason. Watch for it when you're planning overextension. It's a bit harder to pull effectively like Mirror Force (you have to have an empty board to make a plus) but it's easier to trigger.
Call of the Haunted - Same as the above two. It's staple monster recursion for years. Works wonders with Disk commander, especially if you flip Call during your opponent's end phase after he set backrow. Can be flipped during battle phase after you tested for battle traps. Can be chained to Heavy/MST/Dust to get Sangan from Graveyard and search.
Phoenix Wing Wind Blast - PWWB was discovered by Johnathan Labounty and has become staple in Perfect Circle ever since. I like how this card influences the deck. It has two very good sides: First, it lets you deckbuild more freely and not to worry about "dead draws" as you can discard them more often with 2-3 copies of this card. The discard cost is not that much of a downside since this deck can often profit from discarding cards. Second, it can be used to create notorious Raiza Lock which is why the deck is so hard to counter once it gets going. If you spin multiple cards to top of opponent's deck in the same turn, then you're ruining his next one, two or more draw phases. He then gains no resources as the game progresses. If you spin your opponent's Ryu Kokki and then his Il Blud with no monsters on the field, he's going to draw dead cards for next 2 turns. Watch out not to attack into recruiter after creating Raiza Lock as searching for cards will shuffle deck and ruin your Lock. Learn how to use this card.
Trap Dustshoot - Another MVP card from Troop Dupe format that got limited with a very good reason. I don't think you'd like to show your hand every turn because your opponent runs this card 3-of. Anyway, in this format, card got balanced and you're supposed to use it smarter than just "stand-by phase, flip dustshoot". Best time to flip this is in response to search (Sangan, Rota, Stratos mostly) or (in case of late game when game is simplified) as soon as your opponent draws his 4th card. This card isn't called "Holy Grail Trap Card" by many for no reason.
The Transmigration Prophecy - This is D.D. Crow in trap form. It's slower but it's more versatile. It's best used when your opponent plays cards that target in the graveyard, like Premature Burial, Call of the Haunted, Book of Life or Zombie Master. It can also be used to make Malicious live: You have two Maliciouses in graveyard, shuffle one with Transmigration Prophecy and then summon it from the deck. It's good when chained to S/T removal (not being a minus), but it's not used to its full potential.