A 240 welder should have an 6-50 rather than a 5-50.
(The 5 is single phase 120, the 6 is single phase 240. 14 would be 240 with a neutral).

But if you want to use it for general purpose things, then 50 Amp wiring needs to be either #6 or #8 Copper depending on just what kind you are using. Welders can get by with smaller wire than this if the duty cycle is right. So you might be able to get away with #10 if you play your cards right.

Welders generally should NOT be connected to extension cords. (In fact as far as the NEC is concerned, extension cords don't exist).

You're free to run the neutral to the welder receptacle and not hook it up if you think you'll use it later. You're going to have to rework things substantially for the generator anyhow (you do not want to use a suicide cord to back feed the generator, but you knew this since you mentioned the transfer switch).

"A 240 welder should have an 6-50 rather than a 5-50. "

You are right - the plug was a typo. It's 6-50 240 plug, not 5-50.

I'll have to check to be sure, but I believe the welder is marked 40 amps 20% duty cycle and 50 amps 10% DC.

Since I only need 30 amps for future uses (when the welder project is done) I'd love to see if I can get away with #10. Can you point me to the right section of the code regarding welder wire sizing?

I've found Table 630.11(A) in the code which says that the ampacity of the wire shall not be less than .45 times the nameplate primary current in amps (50) when duty cycle is 20% or below for single welders. That number is 22.5 amps. It looks like it's legal to run this off #10.

If there is ANY chance you are going to use this for ANY other 50A circuit, such as a kiln, motor home, range, etc, then you MUST run #6. And considering things like that I'd run a neutral, so 6/3 is my recommendation.

IMO that's the only way to go.

Actually, he needs #6 if he is going to use something like NM. If he runs THHN or the like in conduit, the 75 or 90 C rated wiring lets him get away with #8.
I agree, if you intend to use 50A loads other than the welder, run the big wire.
If you believe that you're going to only run either the welder or later a 30A load, you could get by with the smaller wire.

Frankly, the labor pulling the wire probably makes the slight difference in conductor size negligible (how long of a run are we talking about?).

The welder is very low duty cycle at the high amperage limits, and I'd almost never use that amperage in the project. I may never ever need to run the welder at the upper limits. After the project is over, there is no chance of needing anything at 50 amps. I'm almost certain that I can do the entire project with a 30 amp breaker in place.

As to the run length, I only have to run 15' to get to the near garage wall. I can do some welding right there, but some needs to be done another 30' away, closer to the far side of the garage. The far side would be more convenient for the other future uses.

I had originally thought I'd need to run #6, but honestly it seemed a bit ridiculous for a short term project where my needs aren't anywhere near 50 amps. This is a home welder. I don't need the heavy duty welding capability, and the welder is barely capable of running at 50 amps (10% duty cycle). I've used it enough at the original owner's shop to know that 30 amps will be plenty for the welding I'm doing.

If I can legally get away with #10, I'd install the welder 50A receptacle on the far side of the garage (total run is about 50' to get there) and avoid the need for any extension cord for the light welding needed at the farther distance.

If I have to go with #6, I'd probably only run the short distance - which is where the RV socket is currently located with a #10 extension plugged into a 20 amp 120V receptacle fed with #12.

The NEC has a separate article (630) for welders, and the wire size is no longer tied to the breaker size as in general use branch circuits.

Just as with motor circuits, the breakers are only providing short circuit protection to the branch circuit conductors, not overload protection.

Even with NM you are allowed to use the welder article.

Determine what the arc welder article requires, then go from there.
You can always use wires larger than required, and you may want to do that based on future use.

Thanks for all the help and comments. I managed to locate the installation manual for this welder from the manufacturer's website. It requires #10 for runs of up to 100' and #8 for runs beyond that. I'll consult with the electrician before making a final decision on how I want it wired up.