Use the wire calculator supplied by someone. For a welder & a couple lights & an outlet or 2 you need 60 amps of 220v. Would cover most situations.
Distance is an important thing in sizing wires. Longer the run, the more voltage drop, and the more abuse you give to electric motors if you undersize the wires. In addition to heating the wires, and fire danger, etc.
Looks like #2 copper or # 1/0 al would be the ticket, but play with your numbers yourself. Al is the standard these days for main feeds, just be aware of the connection issues. Would not want it for runs in buildings, but for the main service runs...
Looks like the #6 wire suggested to you would only supply 20 amps at that distance, which is basicly one 110 curcit & 1 lighting curcit. Not nearly enough when you mention 'welder', and not worth fooling with, most of your expense is in digging, boxes, etc. So you save a couple bucks, and end up with nothing worthwhile.
I just had 750 feet of underground, plus 700 feet main service put onto my old farmsite. House is 100 amp, all buildings are 60 amp, and the main is 200 amp, with several junction boxes here & there with 200 to them. Some of that al wire is bigger than the water pipes.....
Sounds like you have an electrician lined up, don't bother the power company, at least around here they are only interested in their stuff, not commercial work. Find an electrician to do these major hookups, then the indoor wiring you can maybe do yourself with a little training.
--->Paul