Ok, I have plenty of experience with this matchup and I use both characters so I'll contribute some words. ^.^
Peach: Her air game is heavily restricted from mid-long range due to Samus' zair and missiles, so the most efficient way to approach in the matchup is to powershield missiles and the zair (if you have the timing down, that is). By doing this, it opens up opportunities for Peach to get in close to rack up some damage with a short hopped dair, nair, f-tilt, slaps, or a grab. Dash attacks are also a good choice to get in close and interrupt Samus' rhythm, so make sure to pop her with one before she has a chance to effectively zair you (similar to its use against Marth's fairs).
It helps to have a turnip in hand when you approach Samus on the ground, because glide tossing is a good way to immediately close in after you shield a zair/missile. If there is an opportunity to punish samus with a floating dair, then by all means go for it, but be wary of her Up B OoS if she has her shield up. Bait smashes and missed UP B attempts from Samus with Peach's double jump, and punish accordingly. Watch for any potential charge shot lead-ins. Toad against any obvious opportunities.
Samus: There is one key word to remember against the Peach matchup...Restriction.
Restrict her air game (floating aerials, spaced fairs, or just jumping in general) with zair and homing missiles. If she happens to be in the air and is up close, you have three decent options to retaliate with IMO: nair OoS, Up B OoS, or a retreating fair/bair. Samus' uair and dair have their uses in the matchup, but are more situational than the rest of her options so use them only when there is an obvious opportunity to. Be very careful of Peach's u-smash and u-tilt. Avoid being above her as much as possible, also because she can punish airdodges very well with her nair, fair, uair, and u-smash. Some Peaches may try to creep in with a bomber once in a while, so be alert to make them miss and punish hard with a f-smash/d-smash. Be sure to sneak in a charge shot or create an opportunity for one amongst your missiles and zair barrages.
Most of it is common sense, but I hope it helps to contribute.