My recommended set for trying to get that first extra stage clear :
-Vampire Fang
-Sannyo pipe
-Eirin Elixir
Imo it's one of the stronger non-centipedes sets this game has to offer. To illustrate, it allowed me to get my first extra stage clear without much practice AND also allowed me to get a Lunatic clear THE FIRST TIME I MADE USE OF IT. Sannyo pipe only produces life pieces after capturing spells, however using active cards (besides Fox girl card and Subterannean Sun card) do not fail the spell : how the set works is as such : you use the Vampire Fang to deal MASSIVE damage to the boss during their spellcard phases, use the bit of skill you have to get through that remaining lifebar and get a life piece, and the lives you gain from this allow you more misses thanks to the Elixir, since you get a bunch of bombs for every lives.
Sannyo pipe is a bit redundant in the main game, where you may just buy lives instead of relying on a card that requires you to have a high skill in order to get some life pieces, but extra stage involves so much spellcards that it's relatively easy to get value out of it ; and Vampire Fang cheese just boost the potential of getting that value.
Alternatively, you can also try :
Number 1 :
-Kicchou card
-Lawyer in Hell card
-Whatever you're comfortable with
The Elixir is slightly limited by the fact that there aren't a lot of opportunity to get bomb pieces in the extra stage. However, there's A LOT more opportunity to get money in the extra stage, especially with the Kiketsu Matriarch's treat : you'll get A LOT of cash to sustain the Lawyer in Hell tank playstyle.
Or also try this other set :
Number 2 :
-Vampire Fang
-Eirin Elixir
-Okina card
No further comment for the Vampire Fang and the Eirin Elixir cards, but Okina's card can prove to be especially strong too in the extra stage, as it provides extra security against a number of bullets that comes from the rear.
As for the main game, the truly good sets are generally the ones with 3 cards (although I can try to recommend some 2 card set ones). You first need to unlock the 3rd item slot by picking Chimata's ability card at the stage 5 item shop.
Recommended set for trying to unlock the 3rd card slot :
Number 1 :
-Barley Rice
-Narumi Jizo
An extremely safe set that grant you a bunch of ressources. Make sure to buy the Lucky Cat card at the end of stage 1 and hope it nabs ya a Phoenix Tail card.
Number 2 :
-Sannyo pipe
-Vampire Fang
Same logic as what I mentionned for the extra stage.
Number 3 :
-Barley Rice
-Lucky cat
A set that is literally about trying to luck out in the shops and getting either the Phoenix Tail or the Narumi Jizo
Number 4 :
-Eirin Elixir
-Patchouli card
A set that's about tanking bullet and trying to have as much lives remaining for the final stage. Only buy lives with this set (or better yet : phoenix card) if you're not sure your skills can help you beat the final stage
The only issue in trying to unlock the 3rd card slot lies in you losing all your ability cards for the final stage, but the ressources you get from the cards do not go away : if you're trying to unlock the final slot but are unsure about your skill, some kind of ressource build is your best bet.
Another one that I would not really recommend, but still can be put to use :
Number 5 :
-Lily White card
-Vampire Fang
Lily White is a very risky card to pick as she shoots bullets, moves a lot and is so tanky she is capable of surviving long enough to give you some trouble. That's where Vampire Fang comes in : you use it on Lily just after you summon her, then boom : free ressources : Lily White doesn't exactly allow you to build up ressources as conveniently as the other cards, but her true value lies in her being able to drop LIFE PIECES every 3rd time she gets summoned : if you're capable of summoning her on cooldown and poking her with the Vampire Fang, you can get a lot of value out of this, especially if you manage to find a Sutra Scroll card to shorten its cooldown. And besides, putting Lily aside, Vampire Fang is still an excellent card for the main game as it allows you to just more or less cheese the game by dealing boatloads of disgusting damage ...
Finally, in case you don't have some of the various items from my recommended sets, here's one that's extremely useful for grinding and finding items :
-Lucky Cat
-Takane Wallet
You basically play stage 1 over and over and buy whatever item still got the "new" mark on them. Simply buying an item is enough to allow you to equip anytime you want, once the achievement for getting a particular item pops up, you can leave and try again until you find more items. If you don't die by the end of stage 1, you should normally have somewhere around 250 or so gold items and somewhere around 2.50 power. Since Takane's card literally halves the prices and since the costiest items in the game is normally 450 gold items, this set will allow you to buy anything you want AND give you higher chances to run into new items, and all of that straight at the end of stage 1 (you can even do this on lower difficulties for further abuse).
Aside from all of that, as far as 3 cards set goes, here are some recommendations for the main game :
-Froggy bullets equipment
-Sanaek bullets equipment
-Mr Wolf passive
For when I play as Sanae. A super Sanae build. It's something I generally play with when I feel like actually playing the game instead of cheating making clever use of game mechanics. I've accidentally no miss cleared extra with this baby (but bombed and Subterranean Sun-ed a bit), so it's most certainly quite viable and also quite fun too.
Another different set I rely on when I do Marisa Lunatic would be
-Reimu aimulets equipment
-Sanaek bullets equipment
-Shangai doll equipment
Marisa do correct damage but really struggle against multiple enemies coming from everywhere. The slow bullets plus suicide bullets in stage 2 doesn't make it any easier either ... it's a bit of a convenience build that sort of circumvent Marisa's narrow shot issue.
Another one that can be of use but is quite cheesy :
-Fox girl card
-Barley Rice
-Sutra Scroll
A cheesy and super bomb spammy set that enable you to bomb your way to victory. This game's no miss achievement does not take into consideration the use of bombs nor active cards, so this build is definitively one of the stronger non-centipede build you can rely on in order to get that achievement.
Another one that can steamroll the game if you manage to properly pull it through would be just ANY centipede build :
Centipede set 1 :
-Centipede card
-Eirin Elixir
-Raiko drum
Centipede cards demand a no bomb run lest it resets, while the Eirin Elixir consumes bombs that you won't even be using in a centipede run in order to save you (not to mention not even resetting the Centipede's damage multiplier) : these two cards synchronise quite well. You can rely on the Raiko drum card, which has low cooldown and therefore is pretty spammable, to be a replacement of sorts for the bombs (as it doesn't reset the centipede damage multiplier either). You can also replace the Raiko drum with the Miko card, the Zener Cards, even the Clownpiece Moon or Patchouli's card to further help protecting the build up of the damage multiplier.
Centipede set 2 :
-Centipede card
-Eirin Elixir
-Lawyer in Hell
A somewhat safe one. Neither the Eirin Elixir nor the Lawyer in Hell card are guaranteed to show of in any given run, so picking them both is good, is they'll both allow you to have more misses. The only problem is that it's a bit harder to sustain either of them ...
Centipede set 3 :
-Centipede card
-Eirin Elixir
-Patchouli card
A at-least-one-miss-per-stage-allowed kind of build that guarantee a bomb for the Eirin Elixir lifestyle, but requires you to be quite skilled in order not to lose all your bombs before reaching the later stages. Which can be a bit difficult with how stage 4 is like ... a solid set, but not one I would necessarily recommend if you're not sure about your skills
Centipede set 4 :
-Centipede card
-Marisa Laser card
-Marisa Missile card
Big boi DPS build for the badasses. Super risky, but fun and devastating. Supplement with other offensive type equipment cards.
Also, in order to supplement Centipede builds, ALWAYS pick the Lucky Cat card after stage 1 to increase you chances of getting something that can help protecting you from losing a life.