Beyond the standard "try all of the ones which appeal to you and figure out which suits you best" response, I'll offer my own experiences. Note that these might not apply to you.
The first class I rolled was a mage, as I've always been drawn to magic users. I was rubbish. I gave up at level 12 because I just died all the time.
I started a warlock. Much better. Died considerably less frequently. Leveled her to 23 before getting the "ooh, what about X class" itch.
Druid next. Leveled him to 17. Lots of fun. Easy to play, but not as quick as the warlock.
Priest. Made it to 14. More difficult than the druid - less diverse.
Hunter. Leveled to 17. Like warlock, very easy to level (obvious correlation of a pet class). Not really my cup of tea, though.
Back to the druid - leveled him right up, he became my main. Before getting him to 60 I tried a rogue (only to level 10...can't really comment on playability, but it just wasn't me).
After reaching 60 with the druid I started another mage and took him to 60. Completely different story to my first, basically because by that time I knew how the game worked, I had an understanding of how to kite mobs (to an extent), I knew what armour to look for, how to play in groups, etc etc etc. Leveling a mage from 1-20 is more of a challenge than some of the other classes, because it's only at 20 that you start getting some of the vital survival/mana efficiency spells and talents, but after that it's a breeze.
Next alt was a new priest, currently at 43 (and has been for a long time). Again, a different experience...I knew where to put talents, how to play, etc. Definitely more efficient to level than a mage or (resto) druid.
Since then I've taken a warrior to 29 (lots of fun, perhaps average in terms of time efficiency, above average in survivability), another warlock to 23 (same conclusions as the first) and another hunter to 17 (again, same conclusions).
I'm still yet to take a paladin or rogue above 10 or a shaman above 4, so I can't say much about those.
I don't know if that's any help, but it's the best I can offer!