As far as playing both toons, its pretty easy to control both the healer and the tank, especially if that's all you're controlling.
I'd have most of the healers hotkeys bound to the numpad, or keys which the tank does not use.

You can easily do something along the lines of 1= Heal Party1, 2= Heal Party2, etc... up to 5= Heal Party5.
On 6-9.. make a macro each for.. Renew, PW: Shield, Flash Heal, and Greater Heal.

Priests macro is something like:
#show Heal Name
/assist Tank Name
/cast [help] Renew; [help, target=targettarget] Renew; [target=Tank Name] Renew

The Priest would likely want Symbol of Hope, Fear Ward, Prayer of Mending and the group AoE heal on keybind as well.

Once you learn your healing system, it will be pretty easy.
All the other keys or keybinds are for the tank, which will have 90% of your attention.

The only stuff challenging will be in having your priest auto follow a toon.
If you follow the tank, you can be sure she doesn't get stuck on things another player is not trying to avoid.
If she does follow the tank, then you'll want to break follow so the healer is not in melee range.
Moving more then one toon out of an AoE at the same time can be an issue until you get used to it.
The easiest solution is to have only the main toon bound to the move keys of WASD, but to have all toons bound to the arrow up, left, right, down keys.

Priest and Paladin will work very well together.
As will your Mage and Mage.