Need help choosing a pet bird?

Hiii, i've been thinking about getting a pet birdie since i'm not allowed to have a dog or a cat..or a snake..or anything fun.. So anyways, do parakeets like to be held and petted? Does anyone know what type of bird likes to play with humans? I want a bird that will enjoy sitting on my shoulder.. But I don't want one that costs like $1000 :)