For Arena.. generally, the best teams have shammies.

Most of them, someone plays four toons, and someone else plays a dedicated healer.
From what I've seen, Resto Druids, Disc Priests and Holy Pallies make the best healers.

For battleground play or world pvp, you can do whatever.

If you're playing them all, it will be hard.
The more toon types you control the harder it is.
You'd have 1x Healer type, 1x DK type, and 3x another type.
You can macro them down to a castsequence for PvE dps, and that's ok for PvP too.
But to be effective you'll want to be able to react, not just click the next thing in the sequence.
I'm not saying you cannot do it, just that I wouldn't expect a high rating.

Maybe the best would be 3 more DK's yourself, and have a friend play a dedicated healer.

Generally shammies are good in arena when boxed.... because...
They have massive controlled burst compared to anything else.
They have Grounding Totems to largely weaken caster teams.
They can purge a lot of useful buffs from others.
Heroism is a huge edge.
Tremor is probably the strongest Anti Fear mechanism.
Thunderstorm, Fire Nova and Earthbind are strong control options.
They are very well armored (good vs melee) for a caster toon.
They can support heal when necessary.