Good morning, I'm connecting a Lincoln 225 AC welder to my fuse box using a 2 pole 50amp breaker and I am looking for some comfirmation on my wiring. Outlet has two hot and one ground terminal. The fuse box has the breaker, a common wire bar (white) and a ground wire bar(green).

Am I right in connecting the two hot terminals from the outlet to the two poles on the breaker and the ground to the ground (green) bar? Nothing gets attached to the common wire bar (white). Also, I'm using #8 wire for 100 feet of length or should I go to #6?

Your wiring sounds correct.
I would definitely go with #6. Even though there are special rules for welders, you are still just wiring a receptacle. If you move, or change plans, this receptacle could get used for anything from a large piece of equipment to a kiln that will run full time.
Use #6.