The first thing to ask is what kind of court are you going to be playing on. For most of us, there are two potential options, hard court or clay court. While there are other things to consider such as playing in high altitude, we're going to focus on the two most likely answers.
Tennis balls come in regular duty and extra duty. This refers to the amount of felt on the balls. For playing on a hard court, the extra duty, with its additional felt, will hold up better on the harder, abrasive court surface. On clay courts, the regular duty works best due to less felt on the ball that can pick up clay during play, causing the balls to feel heavier. On watered clay courts, you may notice it even more. Also, with less felt, the regular duty will tend to "get fuzzy" less than the extra duty.
Both types are available in most types of balls such as Wilson US Open balls or Pro Penn Marathon balls.
When selecting tennis balls, you do get what you pay for. There are some low cost balls available at grocery stores, drug stores and non-sporting goods big-box stores. Often, these balls will lose their bounce faster than the higher end balls. The biggest thing to look for is if the ball is USTA approved. Any ball that is will feature this information on the can. The fact that the balls are approved for tournament use lets you know that they will hold up better than the non-approved ones.
As for which type/brand to use, that is something you will have to figure out for yourself. If you get a can or USTA approved balls, for use on the courts you play on, you should find they perform well. That said, ask any tennis player and he/she will have a brand and type they prefer. Try some different balls and see what you think. Like everything else in tennis, it's all individual.
One last thing about tennis balls.
There is a myth about balls that says the number on the ball means something.
The only thing the numbers are for is to make it easier to know your tennis balls from others. If you have a can of #1's and the people on the next court are using #2's, you know whose are whose.