Mercurio's two-step macros (software agnostic) and/or Mosg2's pseudo-priority system (if you use IS Boxer) will get your DPS efficiency close to that achieved by a solo boxer.
Either approach is effectively one-button spam, but you may need to tweak your spam speed or the macro.

Just about anything will work in Battlegrounds.
Two of the same will complement each other better.
And you can micromanage your spells a little more strongly, by going more manual control and clicking something at the appropriate time rather than at every cooldown.
Toons with dual-spec Healer/Off-Spec can be fun and a change of pace in BG's/TB/World_PvP, but generally the same class is easier for healing.

For Arena...
This will be a lot more challenging, but with the 4.1 changes you're much more likely to match up against an equally competent team.
I would probably go double DPS, either win or lose a lot faster... and play the next game.



Rezzing classes are strong for when one dies in BG's.
If you're split, you can run towards the graveyard or have them run towards you.

Fear and dying/split are the banes of boxing in PvP.
But its not the end of the world, especially with Click to Move + Interact With Target.

If your goal is PvP...
I know you said you're not looking at four accounts, but four accounts has been very successful at PvP.
If you were interested in both PvP and PvE, I'd say go five if at all possible.