Golf Balls today are of three kinds - two-piece, three-piece and high performance. The two-piece ball is made of a solid core and cover and offers better distance with slow swing, while the three-piece ball is made of solid core, wound with elastic and then covered, offering more control. High performance balls are for accuracy.
The two-piece balls are designed for beginners and the other varieties are fro advanced golfers. The cover is generally made of Surlyn or Balata. Surlyn is more durable and strong whereas Balata is softer and provides better grip and control with spin. Balata is preferred by most golfers. Two-piece balls are cheaper and highly available. Three-piece and high performance balls are very expensive and designed for professionals and advanced players.
Choosing a golf ball could be tricky, if you choose the ball used by Tiger Woods, it is not necessary that you can have the same handicap that he does. The choice has to be made as per you game style. The wrong ball could give you bigger handicaps and the right ball could make you feel like a champion.
Choosing a golf ball will depend upon your swing and style of play. If you are still confused, you can try each of the varieties for some days at a time and compare the results.
Similar to choosing your golf clubs, choose the golf ball that suits your swing and game so as to eliminate weaknesses and build upon your strengths. Never go by brands, brands are secondary to performance and suitability. Make sure you like a golf ball because it betters your play, not because it was made by Nike or Yonex.