Ah, ok.
The motor running sounds hopeful, increase the current limit and it should stabilize - as the motor spins faster, it generates more back EMF, which lowers the current it takes (relative to not spinning). Yes, I think you're good to go to the mains + lightbulb test (repeating the warnings about securing it so that you don't have a mains powered motor jumping around your bench).
It's hard to know whether it is worth you getting a variac. It depends whether you are going to get decent use out of it for other stuff. The price is much higher than ta replacement motor or grinder. They're useful to have for testing, but a bulb test will usually get you most of the way when testing power supplies on small appliances etc. 1000W is a big one too (although those are probably optimistic watts). You can often find a, good brand used one on ebay cheaper.