Wowzers, what you want to do can't be easily described in a single response, or in any single area for that matter. This method is very much "custom" to each builder, but there are agreed upon methods that work well over others.

I would suggest googling around and checking out the details of other people's aquaponics setups. Also check out here: http://en.wikipedia.org/wiki/Aquaponics

I can give you a few pointers. First off, don't forget LIGHT! You'll need a source of "sunlight-esque" color temperature lighting. You can get bulbs made for simulating sunlight at pet stores (neon type bulbs). Your stuff won't grow without adequate sunlight (or an analog). Also, (important) since you are cycling water between a fish tank and grow-bed you need to be VERY cognazant of potential CATASTROPHIC flooding if you don't take precautions agains things like pump-failure, power outage.. simple precautions like adding air-gaps to pump outputs can prevent back-siphoning etc. The best way is to have the water-level even on both fish tank and grow-bed. This way if something goes wrong, the water-level in both will naturally want to seek a neutral level and you won't end up siphoning your entire setup out onto the floor of your house. ;)

As far as fish type, by nature, all fish are great producers of waste, so it's more a matter of which fish are the most "hardy" so they don't die on you. Remember.. you're trying to merge 2 ecosystems together, so you'll have to tend to the needs of each one separately. The fish will likely need some type of heating, some fish are sensitive to temperature, and too cold will shock them. Too hot, and they can get crazy and aggressive, or just flat out die.
I like Cichlids, because despite being sensitive to temperature, and their tendancy to get aggresive toward other fish that are colored similar to themselves.. they do REALLY well in planted environments and seem to thrive on the plant matter, they are also eating MACHINES, and product a ton of waste, and can tolerate moderate spikes in ammonia, the byproduct in the first phase of "breakdown" of uneaten fish food and fresh fish waste.

Some other things you can try, you can "greenhouse" your planted sections to retain heat, humidity, prevent evaporation etc, but remember to evacuate the air several times a day because the plants will take in Co2 during the day, and release it at night.

Have fun! It can be really rewarding!