The biggest problems you need to watch out for aren't rest combos but throws and aerials that'll get you off the stage. Falcon can do really devastating combos on Jiggs pretty quickly, and depending on the stage, you can even KO her at a grab at 60%. In fact, you probably won't have too much trouble racking up damage until she's past 60 where everything leads to basically nothing. But you can't get overly ambitious and try to rush her all the time since Jiggs can KO you just as easily and at lower percents. And unlike for you, she can combo you to much higher percents. So be aggressive and react by weaving and feinting with dashes while reading her aerial movements. Whenever you find an opening, you go for it and start the combos from there. But just make sure you don't be too aggressive and be careless near the edge. I know that's standard Falcon advice, but you've got to be careful with Jiggs especially. If you're off, a good jigglypuff will keep you off. But enough of that.
As long as you follow everyone else's advice and utilize smart stage picks then you should be fine. Remember that larger stages do allow Jigglypuff to live longer, but more ground also allows you more movement which is critical since you'll need to get good at weaving and attack when she WoPs. Also, a smaller stage may offer you faster knee KOs, but since Falcon's main game relies on being agile and dominant in the air, a smaller stage may hurt you more than anything since Jigglypuff can cover entire parts of a stage with her aerials to keep you grounded, and with nowhere to run the only option you have would be to be patient and attack from shields or with Bairs. Also, you have to be mindful of Jiggs who can techchase for rests. Smaller stages can ultimately screw over Falcon since the smaller amount of space will allow her to techchase him easier.
Just somethings to keep in mind so choose stages with regards to your playing style. If you want faster KOs, small stages. But if you feel vulnerable and pressured by said smaller stages, go big. (King has said before he loved playing against Falcons cause they're easy and said he finds it easy playing against Falcon on smaller stages. Just another thing to be mindful of, but relax when you play since most Jigglypuff players aren't The King.
