Hi , that is a lovely betta you have! Upgrading his tank was a great idea for several reasons! A 10 gallon tank can be heated and kept a stable temperature easier (a steady 77-79 is good) , It gives the betta much needed swimming space(exercise also!), and it is easier to keep the water parameters where they should be!
I would highly recommend getting an api freshwater master test kit with liquid tests if you do not have one already. Be sure to do water changes of at least 25% every week and use a syphon to clean under the gravel.
Like Veloran said , do not get him a female , this will be stressful for both fish and there is a good chance one would harm the other! Bettas in the wild live in large expanses of water and can get away from each other. They come together to breed , but the male soon chases the female away.
I know you are not finished setting up the tank, but be sure to get plants that go all the way to the top of the tank to provide cover on all levels. Bettas get stressed if they do not have enough hiding area and their natural habitat is densely planted.
Good luck on your new tank!