you should get a pet rat!
they're cheap, easy to take care of and really good pets as far as handling goes!
mice and hamsters are also good pets but you have to work slowly to gain their trust! if you want to handle them then you have to get to know the mouse or hamster slowly by reaching into their cage and petting them gently for a while to get them used to your hand touching them! you also have to talk gently to them in a mellow pitched voice but not too loud!
once you've gotten to the point where the mouse or hamster isn't afraid of you then you can pick it up but make sure there's an open area so the mouse/hamster can safely get off your hand first before picking it up!
it takes time with hamsters and mice when it comes to handling them but rats are really docile in that field! the worst thing you have to worry about handling a rat is them pooping/peeing on your hand!