The most common nibs by far are fine and medium, these terms referring to the width of the writing line.  For the majority of people, either of these styles will work well. 

As a rule, the broader the nib, the better it suits large or fast writing and the finer nibs suit average or small writing and maybe slower writing. 

A broad nib can be irritating for smaller writers as it can tend to fill in the spaces in the letters "o", "e" and so on. 

A fine nib tends to produce a sharper, clearer line, but it can look spidery with large handwriting. 

Note also that broader nibs feel smoother and can be more tolerant of different papers. 

Extra fine or extra broad nibs should be chosen with care - they only really suit people who really know what they are looking for.