Thanks, but I guess my next question is what is the smallest generator I need to run a stick welder? Min. Wattage?
Depends entirely on the input current required by the welder. A typical 225 amp buzzbox might have 50 amp draw at max output on AC and 35 amp draw at max output on DC (don't ask me why they're different, I just looked it up recently). 50 amps times 240 volts equals 12,000 watts. But, realistically, if you tried to run that welder on a 12k generator, it's not going to work well, because when you start the arc, there is a big rush of current, and it most likely is going to overload the generator, causing voltage to drop, and the arc is going to fizzle out.
Now, that all assumes that you are going to be running the box at 225 amps, which, granted, is pretty hot for your typical home fabrication situation. But it gives you some idea of how to proceed. Look up the specs for the welder you are working with and find the current draw at your desired rated output. Then find a generator that can provide that current reliably. If your generator is sized at double your desired output, you will probably be okay. So let's say you're going to top out around 150 amps, which is more than enough for 1/8" rod. Assuming a linear relationship between output and input amperage, that equates to 33 amps. That's 8000 watts at 240 volts. You might get away with running that on a 10k or 12k generator, but you might not. It all depends on how well the generator is able to handle the surge when you start the arc, and how adept you are at not sticking the rod when the arc is unstable.
Another thought: some welders specifically say that they should not be run off generators unless the generator makes clean power. You had best check with the manufacturer to make sure what that means before proceeding. I suspect that if you have an old transformer-based welder, it won't matter, but if you are running an inverter-based welder, that's another story. They tend to have a bunch of circuitry inside them that may not be happy running on a genny.
Hopefully, this gives you some idea on the ballpark range, though. I wouldn't even try running a 240 volt stick welder on less than a 10kW genny unless I absolutely had to. Sure, if you run 3/32" rods you can get down in the 60-90 amp (output) range, but you're really limiting yourself at that point, and you're probably not going to be happy.