Stages are a very simple ordeal with Jigglypuff.
Stage Bans
BAN CORNERIA.
You are not a vertical-KO characters. You are the most easily vertically-KO'd character. Cornera has the lowest ceiling by far of any legal stage.
Why would you ever let anyone take you to Corneria?
PROTIP: If you think you are clever and going to get low-percent rest KOs on Corneria, you are wrong. (Unless it's a Meta Knight or you get a clever rest-out-of-airdodge.) Drill-rest is blockable until high percents, so a significantly low ceiling doesn't actually help you at all.
Strikeout
I'm assuming a list of BF, FD, Smashville, YI, Lylat, PS1, Halberd, CS, and Delfino.
First, always get rid of Halberd unless you are fighting Meta-Knight. The low ceiling sucks and the pass through stage doesn't help you as much as you'd think.
Second, get rid of Castle Siege. Jiggs likes small, flat stages where she can easily approach at a diagonal position above the opponent and knock them off the stage to punish their recovery. Castle Siege's statues are nifty for manipulating your stale moves list, but otherwise it makes for a bad Jiggs stage on all three parts.
Third, they probably already got rid of Lylat Cruise for you. It's a terrible stage for any character who relies on consistently canceled aerials. However, it's also a pretty mediocre Jiggs stage, as the platforms don't help you much at all and hurt your approach. Get rid of this.
Fourth, they also probably got rid of Delfino Plaza, but if they didn't, you should. Jiggs is pretty decent on all the platform segments, but not a single landing zone is good for her. No one is going to let you rest them out of the water, although I find it happens often in teams. :D
Fifth, start thinking about what remaining stages are good for their character. If they have spammable projectiles, strike Final Destination. If they can't be approach below it's platforms, strike Battlefield. They will probably strike Pokemon Stadium 1, but it's a good stage for you if they don't.
If it comes down to Yoshi's Island and Smashville, like many strikeouts do, go with Smashville unless they have spammable projectiles, in which case the platform on Yoshi's Island is more helpful than not.
If you didn't have a specific reason against Battlefield, it's probably your single best neutral stage though. It isn't very wide at all, it's flat, and the platforms are all of a helpful height.
Counter-Picks
Adrora is Jigglypuff's best stage. Actually, forget I said that.
Norfair is a great stage. Brinstar is a great stage as long as they don't have vertical KO power. Jungle Japes is good for matchups in which you don't rely on rest at all. Skyworld is good if it's legal, but only against the characters you would expect, not like Meta Knight, G&W, R.O.B., ect. Rainbow Cruise seems like a decent idea, but I personally don't like it and thin kthe other options are clearly superior. (The boat sequence just isn't good for Jiggs...)
People will probably counter-pick stupid stuff against you. As long as it isn't Corneria, because you banned it, because you aren't stupid, you will be fine.
Thoughts?
Stage Bans
BAN CORNERIA.
You are not a vertical-KO characters. You are the most easily vertically-KO'd character. Cornera has the lowest ceiling by far of any legal stage.
Why would you ever let anyone take you to Corneria?
PROTIP: If you think you are clever and going to get low-percent rest KOs on Corneria, you are wrong. (Unless it's a Meta Knight or you get a clever rest-out-of-airdodge.) Drill-rest is blockable until high percents, so a significantly low ceiling doesn't actually help you at all.
Strikeout
I'm assuming a list of BF, FD, Smashville, YI, Lylat, PS1, Halberd, CS, and Delfino.
First, always get rid of Halberd unless you are fighting Meta-Knight. The low ceiling sucks and the pass through stage doesn't help you as much as you'd think.
Second, get rid of Castle Siege. Jiggs likes small, flat stages where she can easily approach at a diagonal position above the opponent and knock them off the stage to punish their recovery. Castle Siege's statues are nifty for manipulating your stale moves list, but otherwise it makes for a bad Jiggs stage on all three parts.
Third, they probably already got rid of Lylat Cruise for you. It's a terrible stage for any character who relies on consistently canceled aerials. However, it's also a pretty mediocre Jiggs stage, as the platforms don't help you much at all and hurt your approach. Get rid of this.
Fourth, they also probably got rid of Delfino Plaza, but if they didn't, you should. Jiggs is pretty decent on all the platform segments, but not a single landing zone is good for her. No one is going to let you rest them out of the water, although I find it happens often in teams. :D
Fifth, start thinking about what remaining stages are good for their character. If they have spammable projectiles, strike Final Destination. If they can't be approach below it's platforms, strike Battlefield. They will probably strike Pokemon Stadium 1, but it's a good stage for you if they don't.
If it comes down to Yoshi's Island and Smashville, like many strikeouts do, go with Smashville unless they have spammable projectiles, in which case the platform on Yoshi's Island is more helpful than not.
If you didn't have a specific reason against Battlefield, it's probably your single best neutral stage though. It isn't very wide at all, it's flat, and the platforms are all of a helpful height.
Counter-Picks
Adrora is Jigglypuff's best stage. Actually, forget I said that.
Norfair is a great stage. Brinstar is a great stage as long as they don't have vertical KO power. Jungle Japes is good for matchups in which you don't rely on rest at all. Skyworld is good if it's legal, but only against the characters you would expect, not like Meta Knight, G&W, R.O.B., ect. Rainbow Cruise seems like a decent idea, but I personally don't like it and thin kthe other options are clearly superior. (The boat sequence just isn't good for Jiggs...)
People will probably counter-pick stupid stuff against you. As long as it isn't Corneria, because you banned it, because you aren't stupid, you will be fine.
Thoughts?