On the subject of whether you should do a drama or not -- in my opinion, it's best to keep the subject-matter light and fun. For first-time filmmakers, usually, you don't have a whole lot of resources. There are a few exceptions to this rule -- some people have large talented crews on their first short, but that's pretty rare. So, if you're like most first-time filmmakers, your 1st short is going to have the aesthetic of a movie that's being made by a first-time filmmaker. The audience will pick up on this. In their head, they won't treat it the same way they'll treat a slick Hollywood production. In other words, they won't really take it too seriously.
It's also true that you probably won't have the most talented cast in the world. Again, there are exceptions to this rule, but most first-time filmmakers just have to work with what they've got, and that usually means an inexperienced cast. Drama can be very difficult for a non-skilled actor to pull off successfully.
So, for those reasons, I think it's usually best to keep the tone light/fun/playfull/goofy.
This is all just academic talk, though. What's most important is that you tell a story that you yourself would want to watch. Do whatever story you're feeling.
Spend some time on the screenplay. Screenwriters really don't get enough credit -- this is arguably the most important step of the entire process.
Plan extensively. Make a very detailed shooting schedule.
Get lots of coverage.
Don't know what "coverage" is? If not, it's time for you to start brushing-up on the basics of filmmaking. It's all out there for free, and google is your friend. Do you know the 180-rule? How about the 30-degree-rule? Do you know what it means to "cut on action"? What is continuity? In addition to all these, you should also spend some time researching the basics of photography (actually, that's where you should start).
Know what you can do and what you can't do. Write a screenplay that you can do.
Keep it short. Five minutes or less.
Rule #1: Have Fun!