I'll double what Minger said...I bought a non-beginner board (Arbor Alt) after being out twice and feel pretty good on it after another three days on the mountain...don't know how I would feel on a beginner board but don't see any downside to getting something a little better and growing with it
As for what makes a beginner board a beginner board, I'm really not positive...I think most of them are a lot cheaper because they use cheaper materials and leave out a lot of the technology advances (or gimmicks).
I also think they tend to be more flexible so they are a bit slower and more forgiving of mistakes...i think a very stiff board is more likely to react to even a slight shift in weight or a slight bump/change in the slope, while a more flexible boards gives more leeway?
Also, it sounds like you want an all-mountain board since you are not spending too much time in the park...something that is directional or a directional twin instead of a true twin...
beyond that I would spend some time trying to demo a bunch of boards to see what you like...