The Army has the least restrictions for tattoo's out of all the branches. They revised there policy in 2006, so you can now have tattoos on your forearms, hands, and back of your neck. (Behind your RT ear is fine.
Tattoos are now permitted on the hands and back of the neck if they are not “extremist, indecent, sexist or racist.” Army Regulation 670-1, which was modified via a message released Jan. 25, also now specifies: “Any tattoo or brand anywhere on the head or face is prohibited except for permanent make-up.”
Air Guard, you probably would need to get the tattoo removed, so I would go with the Army Guard.
The Army National Guard has a couple of Special Forces units that are airborne, but don't count on joining one of them.
You could be a crew chief for a helicopter which is a 15T I believe. They have hundreds of jobs, talk to your recruiter and see what units are close by as that would effect what MOS you would choose and what slots they have available.
Best of luck