I've been messing around with a few different hydroponics for a while, now.
First was one of the kits you can buy- Aerogarden- which is just a flooded system that uses bubbles to put air in the water. Works quite well, and for indoor use, it's the one I will use in the off season. Not their specifc one, but one I made myself. Pretty easy to do- netpot, water, airpump and lights. And the lights on a timer.
Next was the under water one in soil- which I found as the rain gutter grow system. There's a lot of people doing this, and it's pretty neat to do. I was forced to grow in containers due to invasive tree roots runing my gardens. Instead of using house water, though, I have mine fed by rain barrels. Once you get it all sealed up, and then maintain the floats every year, it barely uses water. And requires no maintenence what so ever (as long as you make sure there's water in the troughs every once in a while). Last year, I added another level of laziness to it- by going no-dig in it. Many of the other planters take the system apart, and "refresh" the soil every year. But then I've read about no-dig concepts, and decided to try it for the containers. Now I add a few inches of compost to the top, and that's it. Leave it for the winter, start over in the spring. So far, so good,
That being said, I want more growing space, so this fall, I'm going to convert one series of containers to a full corregated steel raised bed fed from beneath it. I'm a little nervous about stuff getting into the gutters, but if I can put some forced water to flush it, it should work.
The other thing I wanted to try is a specific outside hydroponic system. Wanting to eventually make it solar powered, I wanted to use the one that ran the least. At the start, I tried using aeroponics- using the NASA example of high pressure, small drops. Quickly went away from that as it was not robust- too many failure points. Next tried spraying the roots- same thing. Then went to a hydroponic tower- where the water is just pumped up to a plate of holes on top of the tower, it drips down onto the plants, and that works really effectively.
But... (there are always but's, arent there...) last year I had a pump failure, which I didn't notice for a few days, and that killed everything. So that changed my idea to a different system I'm still building. This year, though, I'm still working with the tower and found a few more things- it's now powered purely by solar and the original pattern was 1 min pumping, 4 min off.
That, as it turned out, was more than my tiny solar set up could handle over night. Way too much on time for the sun. What was super interesting was that the plants didn't get water for a few hours, but didn't suffer at all. Now I'm watering it 1 min pumping, 19 min off. And everything grows great.
And that all leads me to the system I'm planning, but have not pulled the trigger on- a combo of a flooded system plus the kracktay system. Troughs with net cups holding rock wool. Just the very bottom of the rock wool will touch water. So as long as the plants have a root in the water, they will be ok, and if there's a failure, it will take days for the water to evaporate instead of the plants dying in a day.
Almost all of the flooded systems I've seen on line are like 50% on/off kind of cycle. Seeing what happens with the tower I have now, I'm going with- on- however much time it takes to replace all of the water in the system- off- however much time it takes so that the total on time is 2-3 hours total- I'm thinking once an hour or two will be it. That way, my little 25W solar panel, plus batteries, will be able to run the system without stress.
In terms of fertilizer- I used to stress out about it, then I didn't. I'm sure one can get more by keeping the system perfectly balanced, but I'm ok with the lesser for less work. And I generally just feed it with worm waste. IMHO, compost tea will work just fine - just that I use all of my compost in the spring....
So in terms of what to plant- greens are obvious. If you want tomatoes in the hydro system, they take up a LOT of space, so I'd suggest finding some container specific breeds, so that they don't grow so large.
It's pretty fun to experiment. For pump controls, I've learned how to run an arduino, so that I can easily change the watering cycle. And I've let mistakes add more experiments to what I'm doing.