How can I be a good boyfriend?

I (22M) just recently became official with this girl (21F) about a month ago. She is my first girlfriend, so I’m just wondering what I should do now, since this is all new territory for me.

For some context, we went on a couple dates at the end of last summer, but then I went back to my university in another state and she went to study abroad in another country. So we kept in touch over Snapchat and then went out a couple more times in late December before I went back to college. Then when I came home for spring break about a month ago I asked her to be my girlfriend. Because we go to college in different states, I won’t be able to see her in person again for another month, but we’re facetiming weekly and texting/snapchatting every day, which helps a little although I still miss her a lot.

As I said before, I’ve never been in a relationship before. I want to make sure I’m demonstrating that I care about her and am committed because I really do like her and am very happy, but I also don’t want to overdo it and come across as clingy or possessive.