I would suggest a bird, Owls have dps bonus as do bats, Carrion birds have an armor bonus. All three can learn screech and dive, claw, maybe bite (not sure about that). Plus the fact that screech generates some AOE aggro. So if you are fighting three or four things, you can toss a heal to your pet and not worry about taking aggro on a few of them.
As everyone has said a boar is a great leveling pet, Turn off charge if you plan on doing some CC though.
I use a Owl for almost everything when i am soloing, screech is great as is the small damage bonus owls get. The fact that i can have him on three things, one trapped and safely and easily kill all of them while keeping constant heals on him is great! I use a cat for PvP and normal instance runs, if **** hits hard i will bring the owl for the screech debuff. My third pet is a warp stalker, i just like him and think he is kinda fun. They come with an armor bonus so if i am fighting higher level things one at a time i will use him.
The most importannt thing is just get a pet you like, any pet can and will fill all roles if you know wtf you are doing.
hyrdo