As a new player I would suggest that you play either hunter or druid.
Druid is probably the best class (even though this is an opinion) because they are everything rolled in to one. You can fit any roll and can attack as a cat or spellcaster depending on what you prefer. You can also heal or tank, so if you play it you can try everything out to see what you like best.
I started off as a balance druid because it's probably the easiest class to get the hang of until you understand the game. Spellcasters are probably easiest because you can just stand still and attack. I'd go for either druid or mage.
I'd say that the most fun easy class is hunter because you can hit things with your bow and you can tame your own pet to help you.
You should try out a range of characters by just playing them for a few levels to see what you enjoy the most. What's important is that you have fun!
A Death Knight is kind of a warrior brought back from the dead to fight for evil. They're actually pretty cool, you play on the 'bad side' for a few levels before going back to the 'good side'. Anyone can play a DK because you just bash buttons and hope for the best, but they take a lot of skill to play well.
You won't be able to play as a DK until you have leveled another character to 55. Your DK character will then start at the 55 level so you won't have to do all the leveling again.
Just play around and have fun