I would try FoxFarm "Grow Big" its all organic nutes catered specifically towards use in hyrdoponic systems (its pretty much made of earth worm castings and other micronutrients.) Thats pretty much the only one I used...Then I would use "big bloom" for any fruit/flowering plants.
Also, you might want to look into a "cheap" PPM/TDS meter... it tests the amount of nutrients you have in your water solution. I ve got this one:
Hanna TDS/PPM meter
and also these two:
PH meter
PPM/TDS meter
Theyre kind of expensive, but I use them all the time, I even test my water with them, you can tell how much solute you have in your water (and whether its hard/soft). I can also test my Brita filter for when its needed... water out of my faucet is like 300 PPMS (parts per million), lots of stuff in it.. brita pitcher takes it down to like 40 ppms, which is pretty good... I also bought a commercial grade Reverse Osmosis system, which takes it down to 13 ppm... best water to drink and use on plants.
Id reccommend that you dont use water out of your tap, but fresh RO water, or spring water you can buy in the store... it will help, because if your adding nutrients on top of water thats already at like 300 ppms, its going to nutrient-burn the plants, in addition it makes less of the nutrients available in solution for the plants...
For basil, when it is out of its seedling stage, Basil likes to be in nutrient solution that is about 710-1120PPMs, when its young I keep it under 150ppms, and the PH should always be between 5.5-6.5.
and...yeah if there is 3 internode areas total, I would say just take off some foliage whenever it blocks leaves or new shoots beneath it... that way youll consistently get new growth.
Hope this helps!
this is my other hobby.. I LOVE the whole green thumb thing.