The plant stuff is complicated. If you want to put in the effort it can be a great thing, but it means more time and money sent into the tank and there is a fairly steep learning curve. Extra lights and ferts can create algae problems if your not careful. Its not hard to create problems and get frustrated.
If you are interested though, the site that Annonapersona linked to is a great place to start. Take a look at the Tech Briefs on Plant Basics and CO2, then wander about… good info all over the place.
One regular flourescent over a 20g is probably somewhere in the vicinity of 1 watt per gallon (wpg), which is generally considered to be low light. If you add light and don't get enough carbon and ferts in there, you will get algae (get too much ferts and not enough light, also algae). There are a number of low light plants and you could look into starting out low-light while you're learning and add on later. Low light tanks are a little easier to keep in line. More light will mean faster growth and more options.
Plants are made of stuff. Having a small plant turn into a couple of bigger plants means that that stuff had to be in the water at some point to get absorbed by the plants and organized into more plant. So what is this stuff? Mostly carbon, nitrogen, phosphorous, potassium (the macros), and smaller amounts of a bunch of other stuff (the micros). I use the usual set of DIY macro ferts… Spectracide Stump Remover for Nitrogen, NuSalt for Potassium, Fleet for Phosphates. Flourish and Flourish Iron take care of my traces. Tom Barr has a good article on
estimating doses. Chuck Gadd has a
dosage calculator if you want to try and maintain specific levels.
The plants use a lot of carbon during photosynthesis. Terrestrial or semi-aquatic plants can hoover CO2 out of the air. Fully submerged plants have a harder time getting carbon, especially under the types of conditions we like to keep in our tanks. Seachem makes a carbon supplement called Excel. This would be especially good for a low light tank. A lot of people like
DIY CO2. Annonapersona, for instance, has done a lot of research into it and knows quite a bit about how to get it spinning like a top. Personally I found it frustrating and decided to go pressurized, which I'm very happy with.
If you're supplementing CO2 you are pushing it above the level at which it is naturally in your tank. It wants to return to this level. The flatter you can keep the surface, the more you can slow this return down. HOBs can work, it might just be harder to reach a certain level of CO2. Canisters make it easier. Minimizing splashing will make it easier, etc.
The plants use the energy they can get from light to organize the stuff. Any leftovers will be used up by opportunists, commonly different types of algae. Keeping the whole thing balanced is where you'll find the learning curve. It just takes a little time to sort through.
HTH