I think PvP adds a new element to the game, although world PvP has been more or less dead since TBC release (yes, TBC not WotLK). PvE doesn't have the same opportunities as PvP, but I guess all in all it comes a bit down to which player you are. If you hate PvP, then by all means go PvE. I could never play on a PvE server, because I'm primarily a PvPer and love to do those gankwars on places such as Isle of Quel'danas. I don't necessarily gank people whenever I see them, and in fact, if you want to quest peacefully you can do that most of the time since most people questing are doing just that. This is how it is on my server at least.
Being a PvPer myself, I usually leave people who do not have top-end gear (either ~full t6 or at least 2krating req s3 shoulders) alone, and I think most gankers do the same, since there's no challenge in killing poorly geared and bad players.
About RP PvP, I've only tried that once, and my impression was that the server were populated by 3 groups of people: the leetkids who were there to annoy the RPers, the hardcore non-RPers, who more or less are matured leetkids, and the RPers, who have to put up with leetkids constantly trying to ruin their RP. From what I experienced the playerbase wasn't more mature then my primary server, if anything it was less mature. But this is a very long time ago, and things might have changed. I think I can sum it up with: If you really want to RP, go a RP server, if not, go PvP or PvE, depending if you want to be able to fight horde. If you want to avoid PvP on a PvP server, you can do that most of the time.