where to start... string types tend to be a very subjective issue. roundwound, flatwound, groundround or tapewound... the big question.
roundwound strings are probably the more popular type these days. they're a brighter sounding string, similar to a piano string, and tend produce more finger noise because of they're coarseness. they're more conducive to slapping, popping, tapping etc. overall a very bright string.
flatwounds, on the other hand, are a more mellow sounding string. they have smooth feel, very little finger noise and last longer. typically a more old school sound.
groundwounds are the in-between'ers. they still give you a brighter sound with less finger noise and are a string that has actually been ground down to feel little smoother, really a hybrid.
tapewound strings are a metal string that is actually wrapped in a nylon tape material (they sound and feel similar to flatwounds) and seem to last forever. they tend to sound best with an acoustic or semi-acoustic bass.
experimentation is probably the best path to finding a string that sounds and feels best...