Welders do tend to be quite current hungry things so you'd probably need to go for a hefty (and expensive) generator. The advertised peak output (e.g. 4500W) is likely to look healthy but it's worth asking what the duty cycle is - how long can it deliver that peak output for? How long can it deliver, say, half the peak output? If you're welding in very short bursts it might be a bit more feasible. A lot depends on the power requirements of your welder and how long you want to run it for. Having said that, a lot of domestic duty welders will only run for a little while before needing a rest to cool down too. Hand held power tools are much easier for generators to cope with, and I once spent an afternoon wire brushing a friend's boat armed with an angle grinder with a wire brush and a cheap generator we'd got from B&Q for about £130. The generator seemed perfectly happy. The grinder was about 650 W as I recall.
