Man, the biggest hurdle us "newbs" need to clear is conducting an obscene amount of research. You wouldn't jump off a boat without first learning to swim, so you shouldn't jump into growing unless you're prepared to rush out and spend a few bucks to get the proper supplies. I'm in day 16 from the time I germinated, and all I can say is research helped me out a TON. Also, just from asking, a lot of people on here have contributed time and info to really get me going into the right direction.
You're going to have to get a better light system figured out, at the minimum. I went to home depot and bought 3 round reflectors complete with screw in mounts and 6' cords that can plug into any outlet. They support up to 150 watts, and you can hang them, tilt them, or whatever you please. A steal, in my book, for around 6 bucks a pop. And get some higher wattage CFLs if you can. I read that at a MINIMUM you need 2000 lumens per sq ft, and they can use as much as you can give them. Also go for the "daylight" kind as these put off a better color spectrum that your plants need. I got 3 42 watt N:Vision CFLs at Home Depot for 10 bucks ea. and they're really working wonders. I'll upgrade when needed, but for my grow these are working amazing. They're 2300 lumens each, and put off very little heat.
Second. Do not feed your plants nutes for 3-4 weeks, or until they "tell" you that they're needed. I'm into my second week and have only started using a very very very very mild mix for calcium because my plants are showing a slight calcium deficiency.
Third. You don't have to water every day like you think. I've watered mine twice throughout their meager 16 days of life. Get a moisture meter, as it helps a lot in determining when your soil is dry or wet. I got mine at Lowe's for 9 bucks.
Fourth. Put a fan on them babies. This not only helps circulate the air and keeps your heat down, but it also helps to strengthen your stems. A must have in my book.
That should get you started, hope it helps. Check out my grow in my galleries, I got a few pictures up.