First let me say, I don't have experience with the Chicago Electric MIG welder. I do have some experience however with some other Chicago Electric power tools mainly a 4" angle grinder and 1/2 drive electric impact wrench. Although they function, they are very cheaply made. The grinder was so gutless that I had to replace it with a much better Craftsman unit that I bought on sale. I still use the CE grinder but only with a thin cut-off wheel for cutting bolts, etc. while real grinding duties go to the Craftsman. The impact wrench seems to work okay but the electric cord is only about the size of a pencil, not nearly as heavy as you'd expect.
I have a Lincoln MIG welder that I purchased new probably 15 years ago. It's a 220 volt unit and handles .025"-.035" solid wire easily and should handle .035"-.045" cored wire however, I've never used cored wire. My welder came with gas regulator and gauges and I use a Argon/CO2 mix in my tank. The welder works great and should I have a problem with it service is available. It also uses Tweeco gun so consumables are available everywhere. I don't know what service you'd get for the CE unit and don't know where you'd buy consumables except for HF. You might find a good quality used unit, Lincoln, Miller or Hobart on Craigslist for a good price and it may be set up for shielding gas.
Anyway, what ever you buy I suggest buying copper clad weld wire. Weld wire left in a shop (unless it's heated all the time) tends to rust a bit and trust me, even slight surface rust on wire will keep it from feeding.