So obviously you need two open slots on the panel...but there are other details.
Use a breaker that matches the input amperage for your welder. In other words, if it's 30A, get a 30A breaker, not a 50A...if your 30A welder suddenly starts drawing 40A, something is very wrong, and a 50A breaker won't stop it.
Advice from the guy who wired my garage for 220v was to run stranded line, thick enough to run a 50A welder. You might never get a 50A machine, but then who knows...you might find a sweet deal on a big machine, and then you'll have no more than a breaker to change vs running new wire. Electrician will know the gauge you'll need, I don't...but personally I think it's worth taking his advice on stranded vs solid, and running heavier gauge wire than currently necessary, with the correct fuse. YMMV, he had some scrap 6/3 or something, and it was maybe a 10' run from the box to the new outlet, so the upgrade cost me nothing.
In addition to the wire run through the house, consider the req'd length and gauge of your extension from the plug.
It's money, but personally I'd run the biggest damn stranded wire through the house I could afford, way overkill, so I didn't ever have to worry about the gauge of the extension cord in the garage.
Sucks you're so far from the panel, tho. I'm really glad I don't have to run a fat cord through the door to the house anymore, keeping fumes out of the house is IMHO the biggest long-term benefit of getting a plug in the garage.
Is your ceiling finished down there?
'00 Project, constant state of (d)evolution