Basically:
- stability is in the width. Not only the main width but the one-foot-offs too. Imagine a board sliced like:

the real stability is given by the sum of the slices widths (mathematically, an integral sum). You can see that pointed noses & tail will be less stable.
Width is relative to your height. This is simply proportional to your heigth.
beached56, you should not be ashamed to use wide boards. Remember, your height will give you the leverage to turn a 35" board that a midget would think unturnable.
- boxy rails are stabler than thin rails, flat and concaves bottoms are stabler than Vee, etc...
- long boards are easier to paddle (less row), more glide, and easier on take off as you just motor your way in. Shorter boards rely more on timing for taking off.
- volume should be chosen relative to your weight. Minimum to float (Archimedes) is in litres your total weight in kg (you + board + paddle + wetsuit). More than this give more leverage against your feet to gain balance, and is less tiring. 20 to 30 litres more is quite comfy once use to it. Note that it works the other way around: chop has more leverage on a high volume board to tip you off. Picture a board underwater: it is in a quiet zone, away from the chop. But balancing a sunken board is a different (and more tiring) technique, and should not be attempted too early in your progression.
Volume should be proportional to your weight.
More volume will help in weak waves, low volume will be more manageable in hollow waves.
Hope this helps!
- flat rockered high volume boards are stabler because more board is resting on the water, but high rockered board can be stabler in the low-volume boards, as their provide a kind of "rocking chair" natural balance.