I would suggest watching some of the videos from the people who are running Cata Heroics atm. They of course have very successful runs mostly because of their skill but their team composition is also important.

If you want to keep things easy, stick to 4 ranged DPS and preferably, a hybrid class (Shaman, Druid, Priest). That way you can have 4 identical DPS when you are doing PvE or PvP and then switch one into a healing spec in dungeons/raids.

I run Shamans/Pally, Druids/Pally and Priests/Druid as my PvE holy grail teams (Heal/DPS/Tank) and they are all very easy to switch between PvE and PvP.

Also, with the Shaman/Pally combo it is great fun setting your Shamans to Resto, macro heals to your Prot pally and then play flag runner in WSG. It's a blast trying to have the whole team take down your shamans and lets your other 5 people run amok. 4 x earthshield, 4 x riptide and 4 x chain heal is mad to play!

For more challenge and fun, try

Prot Paladin
Arcane Mage
Disc Priest
Destro Lock
Ele shaman

If you are new to WoW , I'd also suggest taking full advantage of this site. If you're not concerned with complexity of inputs, then THIS will be your tool to decide what toons you will play

http://raidcomp.mmo-champion.com/

Good luck and welcome to WoW :P