There are 3 issues concerning the selection of the proper string: Material, Gauge and String Tension.
There are 3 types of materials you can choose for you rascquet. Natiral Gut, Synthetic Gut and Hybrids
Best quality, excellent feel and elasticity, good tension stability and liveliness BUT average durability and some quality loss at extreme temperatures.
These strings have different qualities. They are classified into 4 main categories:
Can be 100% polyester or co-polyester if used along with Kevlar fibers. This is the durability category; the choice for hard hitters, string breakers, and people without arm problems. Expect harsher hits (very harsh with Kevlar) with above average control. Kevlar (aramid fiber) is extremely durable and holds tension very good. Polyester has much more playability, holds tension fair. A good category of string when you're looking for maximum durability and control. Especially monofilament polyester strings are rigid and are preferred by advanced/professional players as they improve their ball control.
This is the basic and most popular string choice in tennis and also one of the cheapest. Crisp feel, good combination of power and control, reasonably durable and good tension holding make these strings ideal for intermediate players who break their strings frequently).
The top category after natural gut. Best overall playability, gentle on the arm, but punishing to your opponent. The fraying (as they wear) may annoy some players. Holds tension fair. A good choice when you're looking for an arm friendly string - absorbs more shock load at impact, with good power and control.
These are the strings that have an added raised band to give the string texture in order to increase string-ball friction during contact and produce more spin on the tennis ball. Ideal for those who want to improve their shot control through topspin.
Hybrid stringing consists of using different strings in the main and cross strings of a racquet. Hybrid stringing is gaining popularity as more players are looking for a blend of string qualities. By selecting different hybrid combinations of string, players can fine-tune the playability, comfort, durability, liveliness and control.
Selecting the Main string
When choosing a hybrid, note that the main string will dominate the overall feel and playability of the two strings. For example, if you are seeking durability, then the most durable of the two strings selected should be chosen as the main string. If your overall goal is playability, then the string with the most desirable playing characteristics should be chosen as the main string.
Selecting the Cross string
Think of the cross string as having an influence on the main string. While you will not get the full benefit of the string's playing characteristics, the overall feel will be altered. For example, a soft and forgiving cross string, such as natural gut or multifilament synthetic, can soften-up a stiff and durable main string, such as polyester.
Selecting a Tension
To further customize your hybrid selection, you can vary the tension between strings. As a general rule, main strings should be strung tighter than cross strings. This is a popular set-up with professional players and is a good way of increasing the size of the sweetspot. A tension variance of 1 kg is recommended (maximum tension variance of 2 kg on hybrid stringing).
Thinner gauges play better, and deliver more power, more control and/or spin (better bite on the ball). They simply feel better and are less stressful on your arm. However, thinner gauges break more often. So it is a good idea to start with a 1.25mm gauge and only if you break it too often move to 1.30mm gauge.
Approximate Gauge diameters:
As a rule of thumb always string your racquet within the range stenciled on its side. A good idea is to firstly string your racquet at the mean tension the manufacturer suggests (if this range is 24-28kg, string it at 26kg). If you need more power in your shots just lower string tension by 1-2kgr next time you string it. If you need more control just do the opposite as higher string tension generates more ball control.
Final note: Keep in mind that decreased string density (fewer strings on the racquet, e.g. 16 x 18) generates more power and spin. On the other hand increased string density (more strings on the racquet, e.g. 18 x 20) generates more control. This has to do with the selection of a tennis racquet as a certain racquet cannot be strung with more or less strings on it.