To keep plants in your aquarium, you need to have decent substrate, decent light. For serious plants keeping, you will need T5HO lights and CO2 injection, but they are not worth it for a 5 gallon tank.
For now, you would want at least 2W per gallon for your tank to have decent lights, on an automatic timer for 8~12 hours a day at most.
For a 5 gallon tank, I would recommend to get slow growing, low light, short plants. No fertilizer is really needed. My smallest planted aquarium is 10 gallon, I don't use fertilizer in it, because all the plants in there are low demanding plants.
Guppy grass is actually Naja grass, it is undemanding, but fast growing plant. It can be planted but the stems break easily. If left floating it provides good cover for fry, and it is indeed used by many guppy breeders that is why they just call it guppy grass. Yes, it will overgrow in your tank.
Most species of Amazon swords are huge. I have two in my 40 gallon and they are too big for my tank. Hope you get the idea. :p
Anubia Nana is indeed good for a small fish tank like yours. It barely grows, stay short, and it requires very little of everything.
