Heh, I was watching these earlier on the Link forum, when your friend posted them.
Anyway...FLOAT CANCEL. DJC is a very situational technique, but Floating really helps all the time. A Peach without Floating is...nothing. Learn that before you do anything else.
Next, you need to stop using Nairs so much. Nair is an amazing move, but you can't use Nair for everything. Bair is really useful against Fastfallers, Uair can be used sometimes, Fair can be a good finisher if you can predict where they're heading, due to the long time it takes for the move to get off. And Dair is invaluable for combos, just float right above your opponents head and use Dair twice and a Nair/Bair, it'll do some damage and lead to a whole bunch of other things. And if they're CCing, then just do a single Nair and Float Cancel it, then punish with a Dsmash.
Other then that...use more Turnips. Turnip setups are really helpful against ranged characters like Link and Marth, getting up close is dangerous without using a few before you rush in and attack. Make sure to try and catch your turnips after throwing them as well as long as you think it's safe, it'll save a lot of valuable time that would've otherwise been spent in pulling out another turnip.
Overall, you're a pretty good Peach. Just keep up the good work.