What length games are best for a relatively new player?

15 minute, 30 minute or something shorter or longer?

What do you enjoy? I'm a firm believer that the best way to get good at time control X is to play a lot of time control X, and avoid time controls Y and Z. So try some different time controls and figure out which one you like. You can always change later.

And do lots of tactics problems.

30 min or longer. But the thing is in long games you should think more if you play a 30min game like a 15 or 5 min your ruining the whole idea of long games

If you aim at improving, then the longer, the better. If it's for enjoyment, then it's up to you.

2 hours

It is 30|30 and 45|45 for me. Play with increment, you don't want to timeout in an easy endgame after a great game. 

Very well said.  I'd say that unless you tend to get impatient at the end of a long game, the longer the better too!!!