First decide which vegetables warrant being grown at home. a lot of them are simply less expensive to buy than to grow. Be sure to compare to organic grocery stores prices too if that is your concern.
Next, other than too contain the heat (or shield the light) I'm not sure the reflective sides are necessary. It seems to me they would just interfere with tending the plants.
3rd, don't worry about electricty coming in contact with reservoirs (whether due to wick systems or not). You have got to keep light off your nutrients or you'll have algae growth problems. Whatever you use to block the light will also protect from electrical accidents. Plus, are you really that uncertain of your ability to attach a wire to a wall that it may fall unexpectedly. **note: I'm really just kidding in the last statement.** None of the basic simple hydro systems are expensive to set up. Proper aero is but most others will cost less than your lights. a basic ebb n flow system (if you decide against just water a blank nutrient) would probably grow everything you want other than the carrots. For root crops, I've read (haven't done it myself) your best bet is to grow them in sand using a drip irrigation system.

a lot of contradiction in hydro on the web (this site included) is because people all have different intensity levels in which they approach hydro. Some take every effort to ensure all due diligence is given to every aspect of the growing system. Others just plop a plant in a bucket of water and change said water every now and again. Neither extreme is necessary but they certainly don't always see eye to eye on how to address issues. Most everyone else is somewhere in between.
If I were going to venture into indoor growing (I use hydro outdoors or in sunny windows only, currently), I would invest in a hood that is sealed on the bottom and place inline vents running across the light to draw the hot air out and discharge it outside.
As for nutrients: If you're going to hand water each plant you do it the same way you would any planted pot. Water when the soil is dry 1" down. I would probably use a middle of the line nutrient concentration of about 800ppm initially recognizing that with time you'll get a buildup of excess nutrients in the medium. So you'll need to flush them periodically. I might alternate nutrients with plain water to try and keep the medium clean.
Anyway, those are my initial thoughts on what you're trying to do. I'm sure other will chime in with their thoughts and experiences and hopefully you'll come away with a better idea of what you're after.