String Tension Effects
Tennis string towards the lower end of the recommended tension range for your racquet. A looser string face will absorb more of the ball's impact. A looser face will also add depth to shots without a full-powered swing.
Solid Core Strings
Solid core tennis racket strings are more durable than multifilament strings with kevlar string technology being the most durable.
Multifilament strings are more elastic than solid core strings. Multifilament tennis strings play better than solid core strings. They do lose tension more quickly than strings with a center core.
Textured tennis strings tend to produce more spin.
Longer String Length
A longer tennis racket string length (or string plane area) produces more power.
Softer tennis strings, or strings with a softer coating, tend to vibrate less.
High Tension Not as Sweet
Basically, higher tensions decrease the size of the sweetspot and reduce the power (thus increasing control a bit). The higher the tension, the more boardlike the feel. Some people like this. Desired tension is pretty much a matter of personal taste, and as you improve the level of your game, you are apt to notice small fluctuations in tennis string racquet tensions.
Thinner tennis string generates more power (Wilson's research for their Sweetspot string disputes this theory).
It is recommended by the USRSA that widebody frames use multifilament tennis strings (i.e. "soft" tennis strings) or gut to compensate for some of the stiff attributes hence better playability.
You can take some of the shock out of your racket. To avoid vibrations try using a shock absorber on the tennis strings.