I wonder if I should also than use a 50 amp breaker? Didn't notice the note at the bottom of that page of the manual that talks about the welder max input being 52 amps - that is with the welder at 250 amps AND the auxillary 15 amp receptacle at full draw. I should be fine. I won't use both at full draw at the same time.
The breaker size is to protect the wiring so you have to size the wiring according to what size breaker you need, not to the capacity of the machine. It all has to be rated to match. Wire size is somewhat limited to run length also but NEC will give you the minimum size wire for whatever breaker that you decide to put in.
I have an old 2002 NEC (info should still be applicable) that lists the following regarding sizing of wire and breaker: I think your machine would fall under item 1. Looks like you would need number 6 wire in copper or aluminum to feed this 50 amp circuit.
(A) Individual Welders. The rated ampacity for conductors
for individual welders shall comply with the following:
(1) The ampacity of the supply conductors for a welder
that may be operated at different times at different values
of primary current or duty cycle shall not be less
than 70 percent of the rated primary current for seam
and automatically fed welders and 50 percent of the
rated primary current for manually operated nonautomatic
welders.
(2) The ampacity of the supply conductors for a welder
wired for a specific operation for which the actual primary
current and duty cycle are known and remain
unchanged shall not be less than the product of the
actual primary current and the multiplier specified in
Table 630.31(A) for the duty cycle at which the welder
will be operated.
