Do a search for fishless cycling. Threads pop up about it pretty frequently, and Diana has a pretty good guide that she posts to most of them.
basically, find a source of pure ammonia, add enough to bring the tank to ~3ppm. check everyday, add enough to bring back up to 3 ppm. check nitrites and nitrates as well. once it gets to the point where NH4 and NO2 are both zero ~24 hours after a 3ppm dose, you are probably cycled.
Another method I've heard of is people sticking a bunch of fry in a new tank, and letting them (and the biofilter) grow into the tank.
I'd second the compact flourescent bulb for lighting. My first planted tank was a 10 gallon with an incandescent hood, and I put in two (low wattage) CFL bulbs, and cat litter. worked pretty well.
I'm concerned the plexiglass will warp, every one I've seen before has warped. I've heard people claim it's the humidity, and not the lights, but I don't personally know.
What else do you need, do you have a heater, filter, substrate and hardscape from a previous set up?