Pro - Being limited to one lens makes you slow down and focus on the symmetry between you and the subject and use you body position to compensate. Fixed lenses can focus to about 3 feet min to infinity. Usually cheaper (Yashica, Canon, Olympus, etc)
Cons - Non fixed tend to be more expensive (Leica, Bessa, Zeiss) save for the Russian Leica clones
Magic question for you is what is your budget?
Welcome to Apug btw