David,
Welcome to the forum.
I have heard of people using a very fine blowtorch (cook's blowtorch type) to VERY CAREFULLY silver solder the links on a standard chain.
Best advice is to avoid 'multi-machines' usually the lathe part is good but the mill part is rarely much more capable than just milling with a vertical slide in the lathe.
You could get a mini lathe and a super X2 mill for that budget if you aren't shy of imported kit, will have teh capacity to build something comparable to a 2" minnie. If you can judge a good machine from a bad one or have a friend who can on your behalf, you can look at second hand lathes/mills.
Neil