Harbor Freight has one that goes on sale from time to time in the $50-60 range... I think if I got one, it would be that one - it's a DA polisher, gets decent reviews, and I'd just be using it once or twice a year like you. Certainly a very budget-friendly option.
I always buy things I'm not sure if I'll need from HF - if I use it enough that it breaks, then I know it's worth buying a more expensive nicer one.