I went all over this argument back when I was looking to buy a welder. I started with the "I can get a chinesium 120v welder cheap, and then if I need more, I can always upgrade later."
Certain folks edumacated me about all this.
Now, with that said, understand, cheap tools are not without their place, and depending on the tool, for the ,as you say hobbiest, they can be just fine ok...but....
Welding is one of those processes where if the machine can't do what you need, you're done. There's no magic you can do with a low power welder. If it can't perform, then you're done sticking pieces together until you can find a solution.
And, to add to that, I have a personal rule that I've learned the hard way about more than once: "Never underestimate how much capacity you think you will only need...ever." As soon as you convince yourself you only need to weld 1/8 material, I guarantee you something will crop up that's going to require you to weld much thicker stuff, even if it is rare or infrequent.
The difference in material thickness changes exponentially even as the thickness only goes up slightly (there's a big difference in 3/16 vs 1/4 material, for example). Welding well takes a lot of power.
If, however, you are in the position to afford or want to buy more than one machine, then have at it. If all you want is one machine, then don't skimp on this one tool. Go 220v, no question.
In the end, i skipped right over the chinese stuff and bought a Lincoln MP210. I liked the idea of multi-process, so that ability is there when/if I want or need it. I have never had anything I;ve had to weld to date that the machine couldn't handle (and I've had to weld stuff I didn't think I would ever have to).
I don't think there's a super massive difference in cost between a good 120v welder and a decent 220v welder. Yes, more expensive, but not significantly so. I see no reason NOT to go 220v.
Now, concerning other tools, like a metal cutting saw vs plasma...eh, I can probably get away with a cheap chinese plasma cutter because if it fails, I do have cutting disks and angle grinders...would suck, but I'm not dead in the water.