First of all, counter-picking neutral stages is ftl. Everyone knows neutral stages so your advantage is diminished, especially this late in the game. 90% of the time there is a better pick anyway. There are so many gay stages in this game (some that should be banned) and it would be a shame not to take advantage of them.
Spacies - Brinstar, then DK64 in that order. The lava and breakable part of the stage and having different platforms to up B onto help. Something about the breakable part makes it really difficult to L-cancel for space animals; it's possible but most of the time they mess up for some reason. Try to be on the top platform first when the lava rises up really high. Don't pick Rainbow Cruise, don't pick Poke Floats, don't pick Corneria, don't pick Green Greens, Battlefield is really not that bad for either of them and neither is FoD if you are playing a really good space animal (these stages only work well against scrubs).
Jiggly - Rainbow Cruise, Green Greens, Corneria, Poke Floats, you have a lot of picks here that completely **** Jigglypuff. Yoshi's Story is good, but be more wary of rests, as they'll kill at any percent on this stage.
Samus - Poke Floats, DK64. Takes away the usefulness of her grapple which makes it so much easier to edgeguard. DK64 isn't a small stage but it's okay. Also, don't worry about the barrel, Samus can bomb her way into it but you get a free hit after so it doesn't matter. You can pick Yoshi's Story too.
Marth - DL64, DK64. DL64 makes it harder for you to die and easier for you to get to a percent where it's difficult for Marth to kill you. Also the higher platforms means less Fsmash tip. DK64 gives you the higher platforms to recover a different way, plus Marth has to sweetspot the ledge, making it easier to edgeguard. Recoveries that go through the stage really aren't a problem, it's easy to see coming and easy to punish.
Sheik dittos - FD if you are better at chaingrabbing than the other Sheik. FoD if you are not good at gay stages and you are worse at chaingrabbing, otherwise pick a weird stage that you have experience on and that will also lessen the impact of chaingrabbing.
ICs - Rainbow Cruise, Brinstar, Poke Floats (obviously). Wobbles or not, they can kill you with one grab no matter what. So don't pick big stages, it'll take longer for them to die but damage percent and stage boundaries mean nothing to you.
Falcon - Jungle Japes? I personally have bad experiences on that stage but some people seem to do well on it. I do well on Dreamland for some reason, even though no Falcon's dislike that stage. Brinstar, Rainbow Cruise, and Pokefloats are by no means bad for Falcon.
Peach - I don't know what to pick here actually. I pick Pokemon Stadium because of the lower ceiling. Yoshi's Story seems like an obvious pick here, but Peach controls the middle of the stage way too well against Sheik there, and Shy Guys can actually change the trajectory of your downthrows. I don't like Corneria because if you get sucked into a dsmash while she's on an angled part of the stage it's 50%. She can't edgeguard you so much and there are low ceilings, so it's not a bad pick, but also if you grab her under the fin, she can tech off the walls, and considering the importance of grabs, I'd like to let the result of them be consistent. On Green Greens she can just camp the middle and dsmash you between the blocks. It works better on space animals but Sheik is still pretty susceptible to dsmash. I'm thinking I should pick Rainbow Cruise on Peach, but I haven't tried it yet.
Any counter-pick ideas for Ganon (assuming they ban FD), Doc, Mario, and Luigi?