I like to run an airstone in my water jug at least an hour before watering my plants to make sure it has as much O2 as possible but whether it really makes a difference I have no idea. Gives me peace of mind and doesn't cost much.
I always used peroxide in DWC before making a chiller out of an old water cooler. Would buy a gallon of 35% food grade about once a year but seems hard to get and twice the price these days. Drug store peroxide has preservatives in it so not good to use regularly on plants but a lot of indoor veggie growers use it.
It doesn't really hurt good bacteria as much as it does bad ones as the bad ones are anaerobic and lack oxygen so the free radical O+ molecule is more strongly drawn to oxidize them and any decaying material as they use oxygen whereas good bacteria and healthy material like roots have plenty of oxygen already so don't attract that molecule. Well draining medium should have plenty of O2 from the air so extra really isn't needed but in the case of hydro systems I'm pretty sure good old airstones running 24/7 is more than enough.