As for the weapon itself, I'll go against the law-enforcement grain and guess that it's a scoped bolt-action rifle.
A bolt-action would also make it far easier to enforce the one-shot discipline that Route66 outlined. The thing that would mitigate against a bolt-action is if there were more than just the one casing that was found with the tarot card (like you said, if the shooter were disciplined enough to not take a second shot, he'd also be disciplined enough to not eject the casing).