OVERVIEW:
Peach is mostly a ground vs ground character because her crouch is good, her shield is good, and she has some really good normals (d-smash, d-tilt). She's also slow, so playing slanted towards straight rushdown is difficult -- especially since rushdown is typically done from the air or through dash dancing. It's easy to get into positions where you could be hit or have to move out of the way so this forces her to constantly be ready to move out of the opponent's way or move in a fashion where getting hit works to her favour. In a lot of ways, Peach actually plays sort of like a super powerful low tier.
That said, unlike a low tier she has some very flexible scary tools at her disposal that let her break this mold. Since the payoff for her to land one of her big moves is so high, opponents often wind up respecting her dominance in close quarters and attempt to beat her on the basis of superior movement. Due to their fear of your dash attack (and other scary moves), "Respecting Peach" for most players involves shielding or maintaining distance to bait or create openings on her dash attack. If you can catch onto this, you can often pull away from them and look for safe turnip pulls (STPs) if they commit to certain baits (and you catch it). They may even approach you if you stay outside their threat range -- since at that point their defensive spacing strategy isn't acquiring them openings either. Finally, it gives you the option of setting up your float and zoning them with it (defending against your float often involves respecting it, which further augments your ability to pull turnips -- are you noticing a pattern, yet?).
POSITIONING AND COMBAT:
In general you want the opponent to be next to you on the ground because d-smash, grab, dash attack, and d-tilt hit all those areas. So create situations where they are next to you or they are going to be next to you in the near future. Be good at dash, WD, walk, run > dash cancel, and walk > turn movements. In general you're going to be turtling because you're slow. You can pull turnips to help goad people into coming in, to create an obstacle by bouncing it off a shield, to create traps by hitting an opponent (and possibly re-grabbing it), to further augment your aerial game by adding a projectile cover, or a combination of the above.
From the aerial side of things, you generally want opponents to be below and in front of you when you're floating because that's where fair hits. Learn how to move well with your float to make this happen. Be really good at WDing, jumping back, & dashing after you land from an aerial move. Be good at jumping with your full dash momentum (means jumping on the 1st frame of your dash) out of dash dance in any direction to be able to get maximum distance expediently (important for slow characters) and be good at backjumping (after inputting jump, hold the control stick back during her jump startup so she get maximum momentum moving away from the opponent -- also important for slow characters, especially vs faster ones).
vs Fox
Learn to SDI drill to avoid follows
Learn to SDI his uair after u-throw uair
Learn to DI his throw behind him to avoid follows
Crouch his nair and bairs that you can't avoid if you're at low percent and then d-smash him / grab him for his stock
Shield his nairs and bairs if you can't get into crouch in time or you're just at high percent and look for a way out of shield (and if he messes up, kill him)
Crouch his jabs into d-smash or grab him for his stock
Shielded jabs = free aerials out of shield or shield grabs
If you can't shield nair or bair or crouch them productively then 2 o'clock DI the hit (I think it's 2 o'clock)
Shield his u-smash and WD OOS grab/d-smash him for it or float OOS into aerial
Shield his u-tilt and shield-grab it if he's in range or WD back if not
If he tries nonsense like WDing into your with u-tilt and you're floating, pull away and aim your fair really far away from him
If you're on the ground, then dash dance around it or WD back a teensy bit into d-smash / d-tilt
Now you're unkillable except by being randomly up smashed or hit by something at 180%+
Be good at chain grabbing
Be good at hitting u-throw --> d-smash at low percents when you can't CG him
Be good at WDing after d-smash
Be good at following up on platforms with aerials and DJL grab / d-smash
Be good at the CG follows on FD -- if they 3 o'clock DI the u-throw at 120%, you can dash+SH --> nair to hit them offstage or you can do the soft dash attack follows (f-throw if they go to the edge with their tech roll or hit them with the semi-hard dash attack for the angle) -- and if they go anywhere else at 120% you can just u-smash or uair for the kill
Be good at dash attack follow ups and WDing / dashing after your dash attack to position yourself to catch him for his tech options and cover his landing area
Be good at WDing to his landing area after hitting a Fair at 0% so you can cover his tech options
Now you can do stupid damage to him with all your important moves
...Got lazy. May complete later.