BGs work on normal server but you will see fewer players in them. If you plan on participating in BGs at all, I would choose Horde simply because they are usually the limiting factor on the generation of the BGs (Warsong Gulch is 10 vs. 10 there may be 80 alliance but only 20 Horde, so alliance will have to wait a LONG time between matches).
Generally Horde are a little better than alliance in terms of maturity, once you get out of the Barrens, but the difference isn't huge. Active Alliance outnumber active Horde on every normal and RP server. My server (Terenas) is approximately a 2.4:1 activity ratio, which means the active population is about a 70:30 split. Just from the sheer numbers you get more dumbasses on alliance, but ratio-wise I'd say the Horde is only slightly better. (I've played Horde side to 60, but alliance side only to level 30 or so)
From rumors, RP servers are less childish, simply because they enforce some rules on what can be in general chat, and what character names can be. I have no experience with RP servers so don't know. Obviously PvP servers attract jerkwads, because really the only difference between Normal and PvP rulesets is that the PvP ruleset encourages being a jerkwad.
I would choose a server based on population, the side you want to play and a guild. Guilds make or break the experience in my opinion. It's important to find one with players who play at your usual playtime and with enough players that you can usually go on instance runs with 2 or more guildies, minimizing the number of random pickups you need.
While battlegrounds has minimized the PvP zergfests at Crossroads and Tarren Mill, I still occasionally see them on my server at Crossroads (rarely at TM). I presume this is because of the long queue times for Alliance on my server due to the population imbalance... they get bored, and decide to invade crossroads, which isn't all that far from the Warsong Battlegrounds entrance. But these don't affect a young character much, they rarely kill questgivers repeatedly, and barrens has so many quests you can keep yourself busy outside of Crossroads for fairly long periods of time.