If your goal is dungeons...

Give yourself a tank capable character.
And, with a different character a healer capable character.

Tanks: Paladin, Druid, Death Knight, Warrior...
Probably in that order, for boxing ease... although anything will work, if you drive the toon and prefer one over another.

Healers: Priest, Shaman, Druid, Paladin...
The Priest is probably the easiest healer to use with the Paladin as the hardest, the other two are close and somewhere in between.

The three DPS...
Can be three of the same, or a mixture.
Ranged characters are generally easier than melee toons.
Because they don't eat as many point-blank-boss-effects such as cleave.




For a pure PvE team, possibly one of:

Tank: Prot Paladin
Heals: Disc or Holy Priest
Damage: 3x Elemental Shaman

Tank: Prot Paladin
Heals & Damage: 4x Elemental Shaman

Tank: Prot Paladin
Heals: 1x Resto Shaman
Damage: 3x Elemental Shaman

Tank: Prot Paladin
Damage: 1x Boomkin Druid or 1x Destruction Warlock plus 3x Elemental Shaman (possibly dual-spec one to Resto).

All of these teams are similar.
The Paladin can one-button spam away, and tank very effectively.
The Shaman or Boomkin/Warlock can one-button mash, and put up effective DPS.
Heals is either a dedicated healer or 3x Elemental Shaman.

You'd drive this composition from the Paladin.
For the ease of positioning a boss and facing it away from the team.
Also to move the boss if you needed to.
Probably have one button which is just the Tanking sequence on the Paladin... and another that is the same thing, but also the DPS sequence on the other toons.

The challenge is the healer.
Probably go with Grid + Grid Custom Layouts + Clique for heals.
But you can assist the boss and cast at that target.
Or have binds to cast directly at your team members.

Run up to a group...
If its trash, Avenger's Shield and DPS spam them down.
If its tougher, Paladin goes in (possibly with Earth Shield (shaman) or Power Word: Shield (priest)) and engages.
And the DPS joins in a bit later.

A dedicated healer like a Priest or Resto Shaman can make things easier.
They have the option to defensively decurse nasty effects off of the tank and other characters.
But you can heal quite effectively with 3x Elemental Shaman.
Having a fourth toon with 3x Shaman, (the Boomkin/Warlock) gets you +8% spell power which means things die faster.

My favorite team for PvE, of all time was:
Tank: Prot Paladin
Damage/Heals: 3x Elemental Shaman
Damage: Destruction Warlock

My current PvE team is:
Tank: Feral Druid (will be Guardian Druid, in Mists of Pandaria)
Heals: 1x Resto Shaman (or 0x dedicated heals; via dual-spec)
Damage: 3x Elemental Shaman or 4x Elemental Shaman.
(This team will also run 1x Boomkin + 4x Elemental for questing/dailies/etc).



A mixed team is very doable for PvE.

Tank: Blood Death Knight.
Heals: Discipline Priest.
Damage: Arcane Mage, Elemental Shaman, Destruction Warlock.

This is one of my teams too.
They're 80th, and need to be leveled to 85th.
The Tank is not optimal, as in... it will take more of my concentration than a simple one-button-mashing Druid/Paladin; but driving from this toon, the team is effective nontheless.

I have Mage Polymorph (humanoids/beasts), Shaman Hex, Warlock Banish (elementals/demons), Priest Shackle (undead)...
Quite a few crowd control options, should I encounter a group that is too tough to just pull...