Not a bad spot to choose from. We've never rented in Hatteras, but have stayed in Frisco, Buxton, and Avon. Avon will have more "stuff" ice cream shops, restaurants close by than Frisco. Buxton of course has the lighthouse, a couple of restaurants, ice cream, etrc., as well as Cape Point if you have a 4X4. As far as the beach is concerned, the beach in Frisco is a bit firmer than north of the point and typically the ocean depth is very gradual, it's shallow a long way out. The surf north of cape point tends to be a bit "heavier," and the sand a bit softer. We tend to go to the beaches that are north of the point. One more thing to think about is where you stay- soundfront or oceanfront? Do you prefer coffee watching the sunrise over the ocean or a pina colada watching the sun set over the sound? Obviously, oceanfront will be a little more expensive. If you have a 4X4 you can rent on the sound and drive onto whatever beach you want.
You didn't mention what time of the year. If in the summer there will be more people and the ocean will be good for swimming, but the fishing won't be as good. If you like to fish and don't like too many people April and October/November are awesome.