Which healer would I prefer?
A good one.
Honestly, I don't think class would matter to me as much. Play the one you like. They all have their strengths, tricks and tactics. If I were pairing for arena I'd look for a priest or druid first probably. But if you don't want to reroll (and you enjoy both the pally and shaman equally) then the pally maybe? Just considering mobility and buffage. Really, whichever one you enjoy playing more would be the best choice.
As far as the resil on the stone keeper shard heirloom gear, I didn't really notice much difference at the lower levels between using that stuff and the "pve" heirloom stuff. The "pvp" pieces do come with more stam generally though. So that's a consideration. I'd not worry about it too much. Grab whatever heirloom gear makes sense and isn't too much of a pain to get your hands on.
What I would worry about though is GET. YOUR. TRINKET. It's the first thing you should buy if you're going to be doing a lot of pvp to level.
Good luck!