= new reply since forum marked as read
one winter in a rental because it was chilly in there. (Keeping that temperature down does wonders for seedlings, so they grow nice and stocky.) Humidity wasn't a problem, guessing because it was Georgia.
In any case, I'd been participating in seed exchanges, and he filled the little space floor to ceiling with wire shelves and lights from Home Depot so that I could start dozens of fun new plants for the new garden/home we were shopping for. They grew wonderfully, but the shelves were beginning to look like a miniature jungles by the time the weather allowed moving them outside.
No edible greens, though, in those years, and doesn't using unheated basement space up in Georgia for winter salads sound like a good idea now. I could literally grow them in my pantry. 
If we were there.
Laura, I don't remember the lighting specs for the tubes to pick up at a big box store, but the specs are on line of course, and unless you're getting a really good one I'd skip things sold as kits. I'm guessing there are two probabilities here: You'll love it and immediately want more growing capability, and to order seeds of other, intriguing varieties. Or you won't and the kit will eventually get put away for some future garage sale. , but probably the first.
An option would be grab a table and hang a light or lights from Home Depot over, cover it with a protective water barrier (picnic table cloth?), add some sheet pans or shallow plastic bins to set the grow pots in. The pots themselves are inexpensive from suppliers. Start the seeds in the shallow ones made for that (less root rot), then after they have a couple sets of leaves prick them out into ones appropriate for the plants. Or assume they'll be okay in the permanent pots, start a few seeds in each one and thin out the extras once they've sprouted.
