I'd recommend you don't get a low end airgun, like most big chain stores carry. There are some very good values out there, but the bottom of the barrel is mixed in with them. They have cruddy triggers, poor handling, awkward sights etc. They won't really do much to teach you the basic fundamentals of shooting, and while they are dangerous and should be treated like firearms, it can be tempting to fall into the mindset that "its only a bb/pellet gun".
There are some airguns out there that are very good, and would get you a very good start too.
I guess the main thing I would use to decide which one to get first is, which will you have more opportunities to shoot? If you have to go to the range either way, then I'd say go with a bolt action .22lr. If you can shoot an air rifle at home, then I'd suggest that first as you can get more practice. If you can shoot whatever you want at home, then I'd probably go with the .22lr again.
Either way, I would start with either a single shot, or some sort of manual action (bolt, lever, pump etc. ). Semi auto air guns, usually run on CO2 which doesn't offer the best performance for serious target shooting. Its temperature sensitive, and inconsistant. Semi auto airguns or firearms both can lead you to blasting away too quickly instead of focusing on the basics also.
I think it would be best to start with a rifle. Its much easier to learn muzzle awareness with a rifle, which is a big part of the 4 rules.
If you can go to a club or something and take a course and try some stuff out that would be best.
If not, I'd recommend you look at Marlin, or CZ for a bolt action .22 rifle. For airguns, I've been very happy with gamo spring piston rifles (really want to get my hands on a new CFX )