There shouldn't be any problem with running it on a 30 or a 40 amp outlet, just make sure that the plug is rated for at least as much as the circuit breaker. Not a big deal to have a 50 amp plug on a 30 amp circuit breaker, but a 30 amp plug on a 50 amp circuit breaker can be problematic.
unless you have the welder cranked all the way up you aren't going to be using 50 amps anyways. For something like that 20 amps of 240 would probably be sufficient, but if you have a 40 amp breaker available I would put in a 40 amp breaker with the appropriate wire to a 50 amp plug.
I have various welder outlets that are 50 amp outlets on breakers that are 30 amps, they're generally on a subpanel and there's only 30 amps available, usually that would be enough for most anything I do. In the shop I do have a 40 amp breaker and I have yet to trip it.
Same here, but Tennessee would be a little too far to drive from up here in New York.
Aaron Z