Not an expert, but I'll do my best to help some.
The most important thing to keep in mind is that Puff is one of the most vulnerable characters in the game. While your recovery and edgeguarding are very strong, and you don't get comboed or edgeguarded for free, you are among the lightest characters in the game, and any damage is dangerous, putting you closer to KO range. However, this doesn't mean that you need to play defensively all the time, since a defensive player can often make attacking easier for the aggressor, since they don't have to fear counterattacks. You can't be reckless, but you also can't be too cautious. Other things to keep in mind are your aerial mobility. use it to place yourself exactly where you want to be, and always think before you move somewhere. Since jumping removes a lot of options, the fact that Puff dominates in the air means that any time you go for an aerial, you need to make sure it's deliberate, or you'll eat a punish for it. At the same time, don't underestimate the advantages of being on the ground. Although Puff's ground game pales in comparison to her air game, having grounded movement and attack options makes it tougher for your opponent to get a read on what you want. It's kind of like a techchase situation; on the ground, you have all grounded options, as well as aerials, but once you jump, although you have a heavy arsenal of aerials, you've made the commitment to jumping, reducing the amount of potential actions for your opponent to read/react to. It's always better to be below your opponent, ESPECIALLY as puff, since it's easier to set up for utilts and uairs, which can lead to rests. Speaking of, PRACTICE YOUR REST SETUPS. this cannot be stressed enough, if you are dropping edgeguards, that can come with time and experience, but there's no excuse for not being rock solid on guaranteed rest combos. If you uthrow a spacie and they miss their DI, you need that to be a rest 100% of the time. Utilts are the same way. Know how to spot opportunities and when you can take them. dropping these separate good puffs from bad. I loaded this answer a bit, so I'll move on. It's a big question.
Inputs aren't a huge deal, whatever you feel is most comfortable for you and serves your needs the best. I wanted full aerial mobility as well as full access to the C-stick for retreating Fairs and such, so I started clawing Y to jump. You might find another method, but make sure it's natural and comfortable for you above all. If you're not comfortable controlling your character, you cannot play your best.
I know that autocancel Nair is useful, practice in 20XX if possible, have it flash on missed L cancel (by the way, your L cancels are very important, obviously) and fiddle with nairing at different points in your jump. Try to land as early as possible after the nair without the flash for missed cancel. This means the autocancel is working. As for general neutral, I'm not really qualified to advise on that.
I touched on this earlier, but a reddit post from Borp always sticks in my mind, where he talks about what he thinks about when he plays. One of the things he mentions is that he always tries to be the person lower down on the screen, since the player with the low ground has the advantage. Puff is no exception. It's much easier to anti-air than to attack from above. I can't really talk too much about when it's better, but as a rule of thumb, approaching from above is a huge mistake. In almost any case, you are at a disadvantage if you are above your opponent, so like I mentioned earlier, if you're committing to a jump for an aerial, you're sacrificing options and safety for an opportunity to use your aerials, so make sure it's worth it. It's easy to take advantage of a Puff that spends too much time in the air.
I'm not a Rest expert, but missed DI on Dthrow can sometimes happen although they have a very long time to react, so most decent players won't miss it. However, you can trap people sometimes if you grab them facing the ledge, while near it. Since proper DI in that situation is away, off the stage, some players will instinctively DI in towards the stage, setting up for a rest. Additionally, if they DI away, they're offstage and you have stage control, so it's an all around advantageous option, although you may want to Fthrow them to get them further offstage anyway, rather than taking the chance. If you mess around, you'll start to get a feel for what potential Rests look like, and it ends up being more about quick thinking and reacting to DI and tech options. If you can get a jab reset on a missed tech, that's a free Rest (or Fsmash, if you're feeling nervous).
Usmash OoS is situational, it's definitely not a brilliant "go-to" option, although if it's not read, it's not terribly punishable. It can lead to a jab reset situation, but not often enough to be reliable. Usmash in general is an okay move. It's not bad, but it's not quite quick enough or powerful enough to be a "great" option. I could be wrong about this, since I'm not the greatest player, but I personally find that the endlag is pretty risky if you don't hit. Use your Noggin, try it out in friendlies and such, see what works for you.
Jigglypuff's ground speed is pretty slow, so a wavedash or waveland is a way to get a burst of movement faster than is otherwise possible. It's not as useful a primary movement option as with Ice Climbers or Luigi, but it's not a bad wavedash. Wavelanding on platforms is a good way to keep your opponent guessing as to your movement, and any unpredictability is a good thing for you, as it makes it easier for you to land your aerials when your opponent is busy trying to predict your next move. Wavedashing is also your fastest option for covering short amounts of space, which make it useful for dodging grounded attacks, or to approach a move you shielded. Sometimes it's even possible to punish a move with Rest by wavedashing OoS. Practice makes perfect as always. Side note, Wavedashing can also be used to avoid Falco's lasers without opening yourself up by jumping over them. Jigglypuff's low profile allows her to wavedash under the lasers.
I'm an unpracticed player, with not a whole lot of experience, so the best I can offer are insights I've put together from watching and practicing on my own. Feel free to correct me on anything if I'm saying anything too off the mark.
