I second the hempy bucket suggestion as a good first try at hydro. I would also highly recommend you avoid anything even remotely organic as far as nutes or additives. No teas, no worm casing, no kelp based crap, no molasses, no Mega Crop, no Advanced Nutes, etc etc etc.
Stick to pure salts like Jacks 321 hydro.
As far as stopping root rot:
1) Avoid anything organic as above.
2)This includes benificial bacteria like hydroguard, etc. Use H202 or chlorine to keep a sterile rez. If you are running Jacks and keep the rez cool, you dont even need much chlorine.
3) keep the water in the rez and buckets cool = 70F or below. For sure the rez water should stay at or below 70F. In your case, with a remote rez in a cooler, you could even keep it colder to be more safe. The water will warm up fine durring the drip process. The buckets will be in the tent, so you cant do much about that.
I dont agree 100% about the once a day feeding schedule. I think hempy buckets do a little better if you let them dry out somewhat between feedings. Not all the way dry though.
However, feeding once a day will work just fine, and is a very safe way to get started. The difference in growth isnt dramatic and not worth the risk of drying out the roots when you are a new grower. Just be sure your buckets are big enough or late in growth they could dry out between feedings.
By the way, stick with perlite if you do hempys.
Good luck!