If it was me, and that is all I was doing was rebuilding a bucket, and not a lot of welding after that, I would just stick with the 120 volt welder and make it work. It just might mean multiple passes, but that is not so bad.
But as welders, there is something to be said for higher voltage. Really, we do not have much to work with. We can change the process (Stick, MIG, TIG, etc), and we can change our filler rod (6010, 6011, 7018, 12018, etc), and we can fuss with out electricity. Those three things are about all we can do. So to have more power available, the more we can work with it.
That is somewhat changing however, as inverter welders now, are getting DC frequencies in the 100,000 per second range and can manipulate it through digital, instead of analog controls. This is fairly new to me, but with the right welder now, a person can do almost as much with 120 volt versus 240 volt just because the conversion process from AC to DC power is so much more efficient. But it depends on the inverter welder too.
People would be surprised to learn that at home I use a AC stick welder for all my welding needs. The reason for that is, as a retired welder, I am used to 480 volts of 3 phase power. Since there is no way I could get that at home, I do not even try, and just get by with an old AC stick machine. But a good weld, no matter how it is made, will hold a lot.