There is no "best" class. Each class has it's own strengths and weaknesses...it all depends on what you want to play.
Fighter: Can stand toe-to-toe with a tough mob and take the hits. However, DPS is low so it's a long fight. Health will get beat down also.
Priest: Can melee with the use of self-heals. They have a few nukes but DPS is low.
Mage: Prefers to keep the fight at a distance. One of the best damage dealers around, however will fold like oragami if the mob gets into melee.
Scout: Very good DPS, especially with rear attacks and a bow (Ranger). However, once mob is in melee, it's nearly impossible to get behind it again. Gets best bang while in a group.
Since SOE added a lot of solo content, it is possible for anyone to effectively solo. And with the Splitpaw Adventure pack that scales to your level, you will always have mobs to kill.
Read up on
this page for info about each class and subclass.