Not a lot of people mention this but practice catching items. It's amazing how much less of a threat those turnips are when you can throw them back on a whim.
Do not ever, ever, ever crouch cancel with a dsmashing peach. It's painful to even think about. ><
The rest everyone else has said already.
It's a lot of throw game with peach. She floats just enough at low percent that I feel like I can really follow up a throw with some sick combo'ing.
I also noticed not many mentioned stomp. The stomp is incredibly good for those dsmashing peaches since she's in the animation so long. You end up with plenty of time to visually confirm it, read a newspaper, make a sandwich, and then decide to stomp. High enough percent and you get a nice juicy bounce. Mmmmmm bounce - > uair x ? - > Knee
Also, a lot of this game is mind game over move priority. If you're going up against someone who try's to place move priority over mind games, you should be able to learn their game fairly fast and start baiting out their big moves. (like dsmash) Read: dash dancing. Remember, you're playing another human. Not peach herself. She will be different in every single players hands.
TLDR Version: Mindgames trump everything. Don't get frustrated and try to sit back and work around her with falcons speed.