If you are like to do dungeons you could pick druid or paladin. Because you can either heal or tank it is very easy for you to find groups. I also noticed that there are many warriors around, but most of them don't like to tank. So if you don't want to heal, but to tank you could pick warrior instead.
If you just want to reach 60 as fast and carefree as possible you could choose hunter. Or rogue maybe. Both are good in PVP situations also. The advantage of the rogue is that you always can pick the fights you want or avoid them completely if you are not in the mood.
I mostly play my druid. This class is very versatile, as you are either a spellcaster, healer, rogue or warrior, depending on your form. Never gets boring because you have something up your sleeve for almost any situation. Leveling is also pretty easy as you are very though as a bear, but can heal yourself if necessary. Or flee in travel form if you got into a situation you cannot handle. Damage in cat form is also okay.