In my opinion 22lr is the way to go for a first rifle, go and shoot the thing all day everyday and just get used to shooting for dirt cheap. 22 is fine for rabbits, grouse, every shooters favorite entertainment gophers, and if you are a good shot coyotes as well (definitely only go for the head shots).
that way you get lots of practice and have absolutely no problem justifying a your next gun purchase
cause you've gotta have something bigger then just a 22