If you look around this forum, you will find loads of posts about choosing boards. These are the main factors you need to look out for:
LENGTH - This depends on how tall you are really. I would recommend for anybody of average height/ build something between 7 & 8 feet. Essentially the longer the board, the more stable it will be in the water, and the easier it will be to paddle.
WIDTH - You don't want to be lying on a needle when you're paddling. Stand the board up next to you and make sure it is wider than you by a few inches each side. Again, the wider the board, the more stable.
THICKNESS - If you can barely see the board when you hold it side on it is way too small. You need something approximately 2 3/4 inches thick. This will be buoyant enough to hold you up when paddling and will be easier to catch waves.
There are a few different types of board -
POPOUTS - These are basically on their way out now - they are heavy duty boards made from hard foam and the heavy fibreglass used for boat hulls. They are strong and heavy - avoid them!!
MOULDED - Bic and NSP make moulded plastic boards, which are quite good for beginners and are light enough to not break your arms carrying them down the beach. They are practically indestructable.
FOAMERS - These are what you get at surf schools - large boards made of soft foam. Good for your first time out but I wouldn't buy one.
CUSTOM - This is a REAL surfboard, it will be hand shaped and made from light foam with a light fibreglass coating. Don't be put off getting a custom board, just because you are a beginner. The dimensions of a custom board are often written on it by the shaper. If you look at the underside, near the fins, you should see the dimensions and shaper's signature along the stringer (the piece of wood running the length of the board)
If you do look at a custom board, then you can look second hand but be careful to look out for some of the following.
Check that the nose hasn't been damaged. Check that the fins haven't been ripped out and re-glassed. (Actually on both these points, you should be able to tell if they have been well repaired, in which case you should be OK, except if the whole nose has been broken off - you'll see a big line if this is the case)
Check that the tail has not been damaged - the tail is important and misshapen tails will affect how the board handles in the water. Also check down the rails for obvious damage.
A second hand board will have lots of dents or 'pressure dings' particularly on the deck where the riders feet go, but they are not a problem. UNLESS the foam underneath is yellow.
If there is any yellow foam, don't buy the board, it means that it is leaking and will get water logged. Avoid like the plague.
Hope all this helps