Don't really play this game anymore, but just had a thought that might start some discussion. I always considered peach to be a character with good ground mobility options with her instant float canceling shenanigans (with a faster dash this would have been even more effective) and glide tossing, so I wondered if her game could be centered around dancing around mid range and trying to bait opponents with a turnip in hand. You can always use her quick forward glide toss to take advantage of opponent's mistakes around mid range and land a grab or some other bread and butter combo for decent damage. Or if you bait them into attacking your shield with bad spacing, you could use some nice juicy OoS combos with turnips. SH>d-throw turnip>instant catch d-throw turnip>nair is a solid combo that does around 30+%, (sorry % might be off, it's been a while) and it isn't too difficult technique wise. There's always z-drop turnip OoS > aerial or if they're close enough z-drop>footstool>float cancel>aerial for a guaranteed aerial. I mention these two because the first is a solid damage builder and the second is in essence, a guaranteed kill combo (at least the footstool iteration is). These are also the most basic and practical applications of otherwise very difficult techniques.
(In theory, you could link the first two down throw turnips with a second jump and two more turnip insta-catch d-throws then nair for like 50%, and the second technique, you could footstool>float cancel>weak bair>jab lock with more weak bairs which is very difficult considering the level of SDI that players seem to possess by now) But that's why I didn't mention these.
In summary, I've covered a couple areas of peach's arsenal which give her an all-around solid ground game. Ground mobility: mixing insta-float cancels with dashes, walking and the myriad of turnip movement techniques let her constantly be mobile and mess with spacing in close range, but she also has a solid forward glide toss that works essentially like a gap closer to break down projectile walls with good timing and anticipation or a good disengage OoS from bad situations. OoS options with turnips: gives her the ability to punish hard and even have a guaranteed kill setup much like diddy with a banana in shield (although Peach has much lower kill potential and more situational options than Diddy). In essence, she becomes a different version of diddy with the same basic game plan of ground control.
Again this is just the mere outline of a gameplan I would utilize for my "ideal" peach if I had the ability to play her at a high level, and because it's just an outline, I don't, for example, know how exactly one would consistently force a badly spaced attack onto peach's shield but I'm assuming that someone else does and finds my input useful. Please discuss how viable this sort of strategy is in practical application (since I did just theorycraft this) and anything else you wish to take from this wall of text. At the bare minimum, if the peach metagame really hasn't changed that much, then all Peach's should learn her effective turnip combos OoS that I mention, because when I was last active these were still not in common usage (granted this was 2-3 years ago).
tl;dr: ramblings of an old brawl player, there doesn't seem much else to read around here, so take two days, if you need it, to read this wall of text. Hope this helps some tireless soul aiming to take Peach to the top.