Generally directional boards are best for freeride (all mountain). These are the most popular types of boards and also the most versatile. Since they are directional, by defenition they are best ridden in one direction (not as easy for "switch" riding). The snowboards tip will be a different shape than its tail..generally the tail is narrower. Also this affects your stance: with a directional board, you will usually stand closer to the rear of the board. This also makes maneuvering easier, especially in heavy power conditions when you need to pop the tip up a bit when carving.

Non direction boards, on the other hand are either twin tip or direction-twin. Twin tip boards are symmetrical and have a centred stance. Directional twin boards have the same shape on both ends but are stiffer in the rear. These boards are best for freestyle snowobarding: terrain park and halfpipes. Oh and these boards usually have more flex than freeride boards.

There are also alpine or racing boards, but I guess this is another discussion.

If I were you I'd go with a freeride board as it is more versatile if you enjoy mainly going down the maintain (carving and speed). Personally I have a couple boards and take them both with me on any trips.

I would recommend getting a directional board. If you do mainly free-riding then you'll get the most of that type of board.