Check what your florescent say's...If not go to Walmart, Lowes or homedepot and buy what's labeled "Daylight or Ultimate Daylight" these are full spectrum and rated at 6500K that's the ideal set up for plants; and get something around 20watts for your tank. These are avilable by GE, Phillips, Bright Effects, Salvina and for normal 18" cost you about 2-3 bucks
No you do NOT need CO2 and dep on your source water maybe not even liquid ferts. Check my tanks out under the aquarium log they're ALL set up w/out CO2, no ferts and low lights
The most common floating plants you will find are frog bite. Also very common and looking real nice is pennywort, cause you can either let it float or plant into your gravel.
For a 20g I'd suggest plants that stay fairly small, if you have driftwood or rocks in there, something like Anubias or Java Ferns. For the back something finer Like Vallis or Rotala; centers are often well planted with Narrow leaf chain swort, Crypts, dwarf hairgrass, kleiner bar sword.....
Here's the site I always buy from you can click on the pictures to enlarge them to give you ideas what the plants look like Sweet Aquatics