"I would have to put pebbles in there to be considered hydroponic? "

No, you would need to use water in there to be considered hydroponic.

That is a neat system but pricey. I have personally never bought a hydro system, I am more of a DIY kinda guy, so I am not the one to ask for referrals of system. Grizz or Rob might have some advice. We will see if one of them chime in.

For the system you linked, you're right though, you would either need to purchase pebbles, or what we call hydroton. Hydroton is a type of expanded clay shaped into balls that are reddish in color on the outside, black on the inside. Hydroton is not only cheap, but it is reusable and pH stable.

Another thing you would need is an air pump and air stone in the main reservoir to keep the water well aerated and from becoming stagnant.

Here is a link that might be useful: Hydroton Link

That's a sub-irrigated planter, and you can make them out of anything.

http://en.wikipedia.org/wiki/Sub-irrigated_planter

http://www.insideurbangreen.org/diy-sub-irrigation/

http://earthtainer.tomatofest.com/

That system is slightly more complicated than a self watering bottom feeder system. It uses a smartvalve or aquavalve" so the moisture drains completely before refilling.
I always thought it was an ingenious device. I scratched out some preliminary designs to replicate it, but never fully developed it. I always thought you could work it out as a flood and drain system that didn't require electricity. simply fill an elevated rez every day or so, then let the valves control how often it watered the trays.
Just to be clear, I'm not saying it is better than a self watering or wick system, just that it is more complicated. The potential is there for it to be a better system, I just can't say I've ever used one to make a comparison. Generally, bottom feeding self watering systems work better with a medium that has a lot of capillary action. I would recommend either perlite or coir as a medium.

from the designs I've seen this system drains to waste. This isn't suitable if you're using hydroponics nutrients. they're expensive and draining to waste would be a... waste.
I have used bucket type hydroponics successfully for a few years. take a bucket and lid, cut a hole in the bucket lid and insert a net pot. put a submersible pump inside the bucket with tubing that either sprays the roots from underneath, or drips from the top. the attached link shows how to set up something similar to mine. but it's more complicated. mine just has aquarium tubing that goes up to the top of the hydroton and flows from the top. I don't use an air pump to aerate the water because I get enough aeration from the water flow.

Here is a link that might be useful: you tube video

Kleem,
autopots are much more akin to a wick system and are not drain to waste. they basically flood a tray to an inch or so, then as the plants consume the nutrient or it evaporates, the valve will only reflood the system when the tray drys out.

@ Keyboarg

Because this system doesn't require electricity you don't need to mess with any timers etc. so it would be suitable for a newbie.

I don't have any experience with this system so I can't comment on how it yields compared to other systems.

But I did find this animation that explains clearly how this system works: http://www.autopot.co.uk/video/autopot-easy2grow-kit-3d-animation

Regards,

Justin

Here is a link that might be useful: Autopot Easy2Grow Video

after watching the animation I have a couple of concerns. first the tray will only hold an inch or so of water. so you'll have to use soil, or something that will absorb the water and get it up to the plant's roots.
also, the plants aren't going to be using the water that quickly, so it seems like there will be standing water in the unit for some time. with standing water the risk of root rot will be increased.

"from the designs I've seen this system drains to waste. This isn't suitable if you're using hydroponics nutrients. they're expensive and draining to waste would be a... waste. "

Brilliant!!

A soilless mix in a container, hand watering with even miracle gro can be considered soilless drain to waste. This is what gives me great results with little work and money. I grow an outdoor chili garden in containers. I do use one hydroponic fertilizer once evrey two weeks high in secondary macronutrients like calcium, magnesium, and sulfur. This gives me fantastic results.

If you run drain to waste and water comes out the bottom which you don't recycle, you a wasting water.
if you water just enough so that none comes out, you're not watering enough to remove the salt build up.