It sounds like you just want to do BGs and kill stuff. So I would say frost dk is the way to go for you. If you are fighting a caster you use AMS, versus a melee you use IBF, on a healer you use NS and for burst you macro use trinket and pillar of frost. Very easy basics, by playing more you can improve the timings of your cooldowns etc.
Another option is frost mage where you kill melee with his own frozen tears, but you need to adjust a bit more to your opponent (which abilities to use etc). I feel that increasing your own skill is more beneficial for frost mages than dks in BGs though.