Firstly, congrats on your betta! That's what I began my hobby with. a half gallon is, unfortunately, way too small for long term use. I wouldn't even add the gravel and the plastic plant might tear his fins (depending on what type tail he has).
For a half gallon, you should clean it twice a week 100%. This means cupping the fish in a small cup (by sucking him into it as the cup breaks the surface, tricking him into it with food or with a net) and cleaning all the water and decorations (which should only be one or two plants and maybe a small terracotta pot). Then rinse everything, fill it back up with water about the same temperature as it was (even a few degrees off can shock a betta fish, I always test it on my wrist) and then condition it. That bottle that came with the tank won't last long!
As for heaters, heating a half gallon is hard to maintain. If it is within your means, I would return the .5g and get at least a 1 gallon tank (or bigger if you can). The heater will depend on that size tank you want to keep for a while.