I've been trying to become an all-around player, but my preferences are to the "attack" classes.
Scout - Running around really fast and ambushing people is good fun, so you know that I prefer to use the BRB.
Soldier - Easiest to team carry. I managed to turn around a 35 minute (total) Turbine match with 2 enemy caps and 0 friendly caps in just 12 minutes by switching to my tryhard Soldier loadout (edit: Also my non-tryhard loadout works in a similar way to puff and sting, and see below)
Pyro - What can I say? Puff and sting and reflecting rockets is a lot of fun.
Sniper is also fun if I'm playing on a silly server that gives points for taunting after killing.