Thanks Tiny ... that is the most common issue when having a planted tank, ALGAE!!!!! ...
You will have to work with it, you are still new and I can say that I was going through the same problems with you. If you can't handle a 20g, what makes you think a 60g will be any better?!
Algae is something that you will have to take some time studying, it may take days, weeks, or months, maybe even years to start understanding how to get rid of it.
The idea is to have your levels in check and make sure that everything is balanced, you first want to start out with plants that grow really fast. Then you can start limiting your plants as time passes by.
But let me tell you this don't give up yet.