I agree with freemangreens. Take it slowly. Grow steadily.
I started off (years ago) with growing herbs in inverted Coke bottles standing in the kitchen window. Very exciting stuff! The next year I made a wooden rack that could take 32 bottles. From then onwards it just took off.
Now I'm in ebb&flow for most of my plants, except tomatoes which are in deep water cultures (DWC).

I concur with what the others have written but wanted to add one other thought. consider cost of the crop. most folkz who grow food for the family do so for financial reasons. make sure what you're growing is less expensive that buying it at the store. usually ground crops are not. (onions, potatoes, carrots, etc.)
As far as how to handle crops with different nutrient requirements. just set up three different reservoirs. Low strength, medium strength, and high strength. then if your flood trays have detachable/movable connects you have a lot of versatility in what you can grow.
Generally speaking greens are low strength, nightshades and cucumbrits are high strength, and about everything else is medium strength.

Thank you all for your advice. I'm still trying to figure out how much a system would cost for me to put together. Any sugestions on systems and costs? What about costs to run over the year?

I finally got my nutrients yesterday and we started the seeds for our first attempt. We are growing salad bowl lettuce and a cherry tomato. We homeschool so it is becoming poart of my Daughters science curriculum. I still need to get ph test strips, ph up and PH down, and the bubble wand, but I figure I can get those at the local aquarium store. Hopefully we will have the system up and runnig before thanksgiving.

pH test strips are important. Some plants wont grow outside their limits. Lettuce will grow well in a float system (a piece of styrofoam sheet floating on a nutrient bath).
If you are serious, the most expensive parts are the pH and the conductivity testers. They're a hundred bucks or so, but well worth it. The rest . . . you can buy "plug-in" systems for a price, but the guys I know all built their own DIY systems, like I did.

for a cheap nutrient solution visit southernag.com. find their product catalog (a pdf) and check out catalog page 6 for a hydro solution. that solution also requires some greenhouse grade calcium nitrate and epsom salts. all together, that stuff may run you $50-$60 but will last a loooooooong time. Well depending on the size of your garden.

want a cheap box. buy cedar privacy fence pickets at the lowecal hardware store to make a frame. (they were under $3 each when I bought them last) Then line it with plastic.
Waterproof outlets are all you though I would suggest browsing the plumbing section. make sure you have an overflow in each one as well as a primary drain.

perlite will probably be expensive so search around for a bulk supplier. alternatively you could use landscape lava rock as a medium also available at said hardware store.

Just FYI, from my own experiments, perlite occupies 46% of its volume (54% airspace) and retains 45% of the water that is poured into it during a flood cycle. that is based on perlite bought locally and packaged under the miracle grow brand.

There's a lot of things you can use as your hydroponic medium. Sand, gravel, even sawdust (certain kinds) can be used under various conditions.

Be careful with what kind of non-hydroponic pH up and down you use. The aquarium stuff isn't bad, but it can potentially cause precipitates in your solution since it's not really designed for use with hydroponic nutrients.

I'd also recommend some moderation in your initial gardening attempts. There's not a lot of expense (beyond personal labor) in large backyard soil gardens, but going large-scale like that in hydroponics will nickel and dime you for months.

When you're comfortable with your current hydroponic system(s), employ the doubling rule. Double whatever you've got until you've got as much as you want. But always wait until you've got mature plants in the new systems before you decide you want to double again.

Everything else, let it grow in the dirt where it's much cheaper. I may grow some hydroponic potatoes or carrots some day, just to see what it's like, but if I want to have a garden of those for eating I'll most likely just plant them in soil.

So that's my advice: Build a "normal" garden and let your hydroponics take it over gradually.

RE: garysgarden response:

Not to change the subject, but . . . I'm currently growing potatoes hydroponically. I'm using perlite in a larger-than-life plastic pot that is sitting in a static system. I top water with aerated nutrient, keeping the bottom 1/4" siting in a nutrient puddle.

Stay tuned and I'll let you know what happens as soon as they set flowers. That's when there'll be "new" potatoes dancing around somewhere under the perlite mound, if it works! I don't know what the actual fruit will look like; maybe teenage mutant ninja types -- who knows?

IIRC potatoes are one of those that really doesn't care too much where it's grown as long as the roots and tubers are kept in the dark. If light gets to the roots you won't get any potatoes.

But I know lots of people just heap straw up on their plants to keep them making more and more taters so I doubt the density of the medium will make much difference.

I look forward to seeing how it works for you, though.