Well, invincible means you're incapable of being beaten, invulnerable means you're incapable of being harmed, unstoppable means you're incapable of being stopped, and I'm not sure if infraggable is even a word but I assume it means incapable of being killed/dying.
I'd go with invulnerable, since it seems to be a bit more open to experimentation than invincible or unstoppable. Invincible just means that you'll never be beaten in a fight, so you could still die if you jumped out of an airplane without a parachute, or had some kind of terrible accident happen to you. Hell, you could be invincible and get killed in a car crash, not exactly a good time. I'd be wary of "unstoppable" because it might take the literal meaning and make it literally impossible for me to stop moving, which would suck. Invulnerable on the other hand means that I would never be injured by anything, no matter what kind of stupid thing I did. I guess infraggable would do the same, but infraggable means I would never be able to die, even if I grew tired of life, which could backfire and turn into my own personal hell.
So invulnerable it is.