if you want to invite someone to visit me....

it's better to use "приезжай ко мне" (come to my place) or "приходи ко мне" (this one is used when the physical distance between you is not big).

if you are to choose between навестить and посетить you must use "навестить меня"

 "посетить меня" is awkward, too formal, and is not likely to be used referring to self.