If you want to do this legally it's going to cost you more. If you want to get up and running your on the right track, but here are some things to consider: (in Canada at least and I could be wrong on a couple of these)
1. If your wire is not consealed in the wall it will have to be mechanically (conduit,BX or Teck, etc..) protected if located in an unfinished area.
2. I'm pretty sure you can't wire a regular 15 amp outlet on a 30amp circuit, you will need the proper plug configuration as a 15amp outlet is not designed to carry that type of current.
3. If this outlet is in what is considered a damp location or outdoors, it has to have ground fault protection (at least on a 15 amp circuit, on anything larger I'm not clear on this).
4. As before wire colors can be marked with tape to indicate proper color.
5. If your welder has a standard household 120 volt plug end on it then that is legally all you can feed it with, whether it be the regular 15 amp or the 'T' type combo which can be 15/20amp which is now standard on kitchen counter outlets.
Just for reference: I'm no angel as I just had my insurance inspector show up yesterday unexpectedly and got caught using 12/3 SOW cable to feed a construction heater I put in, wired into my panel in my garage. I used the proper plug but should have knew better on the wire even though it is consealed through the back of some cupboards. The heater cord itself is only #12 wire but has a 30amp plug end on it. It draws 19.7 amps so I protected it with a 30amp breaker as a 20 would be tripping all the time. It's all I had that day and I got lazy and left it that way. Stupid, yes but I'm glad he picked up on it as I had really forgotten about the wire size. It will be changed this weekend. The only other thing is why CSA/UL allows these wire size descrepancies unless the cord is some finer wound wire with a slightly higher current carrying capacity than regular #12 wire.
Steve