Stage Strike: Battle field is probably a bad neutral to take her too, because I am pretty sure her downsmash goes through the platforms and that can really mess us up since we like to approach in the air. Final D gives ZSS great control of her projectiles in the begining of the game and can help her later with no platforms to help avoid her side-b/downsmash. Smashville really isn't that bad, plus it can catch some of the projectiles, which can be a positive and a negative thing. Yoshi Island brawl probably helps her with the tilting platform and stuff, because if used right, it can be a great advantage to either character. Her downsmash also goes through it if I remember correctly, so thats a very bad thing if you want to... you know... air approach. Although, the tilting basicly makes the pieces go away if they are thrown once. Smashville is the best choice in my opinion. Zero Suit Samus is going to try to space side-b's, so if you take her to smashville, you can jump around on the platform to avoid it, and then punish afterwards. Avoiding the pieces on smashville is way easier because she now has to throw them either down, up, or jump -> forward throw, because now there is a platform, and if she chooses to jump -> forward throw, thats one piece gone, which makes the begining of the game so much easier.
Counter Pick: For me, getting downsmashed = death, so I would want to counter pick Zero Suit Samus to frigate instead of japes(and I myself don't really like japes either). Frigate has the stage switch that can really mess Zero Suit up more then us. Plus, one side having no ledge = really easy gimping. Japes does have many ledges, which makes gimping Zero Suit Samus impossible, but spacing side specials is also very hard to do because of said ledges. I don't know enough about japes to argue it any further. If you take a Zero Suit to frigate, I'm pretty sure they will camp the left side until it changes, so they have way less of a chance of getting gimped. Try to get them to roll to the other side, or put so much pressure on them that they have to get away some how, which could be going to the other side or just a downsmash, which can be punished. Once she is on the right side, just keep on doing kirby stuff. space airials and stuff. when she gets off the stage even slightly, try to down air/back air to keep her off of the stage, since she can't really recover. After the stage change, avoid being in the middle, because her downsmash can catch you with the way the stage is formed.
Ban: I would ban Castle Seige, because she has more control of it then we do in my opinion. The first stage is basicly a free forward special spacing, dsmash is really easy to hit, pieces can be abused really badly, that type of stuff. Second stage has the statues which makes avoiding everything so much harder. Third stage isn't really as bad as the rest of it. But yeah, avoid this stage against ZSS. Battle Field/Final D are also pretty good for ZSS. Mansion is good too, but its barely legal, so you don't need to really worry about that.
Sorry if all of this has been said, or some of it is wrong. I'm just trying to contribute ^-^.