Air dodging mid air, not to be confused with the grounded spotdodge, lasts long enough to safely pass through Link and Toon Link's Up B moves if they are using the move midair, because they're going up and you're going down.
Now, if they are camping out the spot on the ground you want to land on, those long lasting moves are rough on air dodges. That's why I mentioned the ledge though, if you air dodge towards the ledge, you'll be safe from most grounded landing punishments. Then your options improve because you can get up normally, roll on to stage with L, attack onto stage ledge jump aerial attack, ledge jump air dodge, letgo double jump air dodge, let go double jump aerial, and with some characters even just attack from the ledge.
Of course, the funny thing about Peach is she doesn't have to land, she can use her float ability by pressing holding jump and down. (something like that. You can go to smashboards character section and read guides about peach for details about her, I mostly play against her.) Doing that can get you over to the ledge virtually whenever that's where you want to be. You can also use Peach's forward air while you fall away from them, and that's pretty hard to punish since it has so much shieldstun.
Peaches tend to like to stay low, but not all the way down on the ground. Being on the ground lets you glide toss turnips (interrupting a roll with a throw, causing a slide - an advanced tech that's not hard to do and almost always better than a throw) and use her grab against opponents that are shielding a lot. Her other ground moves are mediocre except for punishing. (punishing is when an opponent misses you with an attack, giving you time to hit them with no risk.)
Peaches spend more time floating just above the ground, or a little bit higher, at about head height. Some characters will take a beating from repeated floating down-airs on their head, even if they shield. Forward airs from a floating peach are pretty safe and hit hard. Nair is about as fast as her jab, but pays off with much more damage when it connects. Since you asked about which phases of fight to use aerials in, the answer is both. All her aerials are useful racking damage, and Neutral air (nair) and forward air kill. (You might want to keep one of her killing aerials "fresh" though, recently used moves have decreased knockback and damage and won't kill as well. Nair and forward air are generally easier to hit with than Peach's grounded kill moves)
If you aren't floating like crazy with Peach, you aren't anywhere near her full potential. The jump between ground game and floating and back again drives me crazy but to lots of people it make Peach very fun to play because she has two "modes". That makes her tough to master too though, it's almost like learning two characters.