Process is more important than result.
Just do it.
You will like it.
Although it's seem like to be a failing result.
President of USA Barack Obama often says "Yes,you can"

I'm new to hydroponics myself, but I stumbled across this recently and bookmarked it. I would still like to try it, but haven't yet myself. I'll post a link below.

Here is a link that might be useful: Frugal Hydroponics

I agree with luvahydrangea,
if your looking for a simple type system, as well as inexpensive to build, I would also suggest a water culture system. I built one for about $20 that to grow 8 heads of lettuce. Not that the other 5 types are difficult or expensive to build, especially on a small scale. But the water culture system has only one moving part, and it's easy to see the roots (good visual for the kids). Not to mention easy for kids to build themselves, as well as understand how it works.

I also think that a DWC system will be the most cheap and easy to build. You can grow a variety of plants in it and the only "con" I can think of is keeping the nutes within the correct temp range; roots don't like to be too hot or cold.

Build it yourself for the fun, cost savings, and education. DWC's are the easiest (to me) and an ebb and flow is just plain cool when you build a good one.

Post some pics and share your success!

Here is a link that might be useful: My Hydroponic Adventure

I'd suggest an Ebb & Flow (Flood & Drain). Can put together one with two tupperware bins, a water pump, and a flood/drain kit. They are very simple in design and of the different forms of hydroponics, seems like the least likely to encounter issues(although I'm sure someone will debate that).

Couple the above with a one-part nutrient formula to keep it simple. Perhaps KoolBloom/KoolGrow.