I was about to start a thread on using my Lincoln 225 AC 'Tombstone' welder on a 4 KW generator when I saw this one already open. Kinda wish I'd have read all this good info before my own 'field trials', it would have saved me a lot of guess work. Coincidently, I have that same Generac 4000 watt generator and at first tried welding using 1/8" 6011 rod, man that was an absolute no-go as that sized rod at > 100 amps shut the generator right down. I had some stock gates that needed to be modified right away, so I went to Home Depot and rented a little 110v Lincoln wirefeed machine which worked fine on the generator, but marginally got the job done.
I still wanted to be able to use my stick welder for future jobs, so I started a little experimenting. First I bought some 1/16" rod and dialed the old AC Lincoln down to 40 amps. Presto! a nice arc and near perfect looking beads, but only good for really thin metal and those 1/16" rods burned up very fast. I figured the 'sweet spot' would be 3/32" so that was my next move, and it worked very well.
Bottom line for me was 3/32" 6013 rods at 75 amps for welding 1/8" stock. Actually pretty good looking welds and not overworking the generator, I was able to weld for prolonged periods of time. As others have stated, its a little tricky starting an arc using this small generator, but I found myself getting used that with practice, so its not a real problem. I like my stick welder, and this combination allows me to be mobile around the ranch, albeit somewhat limited on welding heavy stock.