All that Mac will run is El Capitan but it will run very well with as much memory as it can use and an SSD. However, you ought to decide beforehand exactly what you intend to do with it. Most games will require a more recent operating system, and Mail seems to be having trouble coping with recent email security protocols (apparently; Mail's problems arose only recently).
So yes it will run well, but it will never be capable of doing something El Capitan can't do.
Upgrading from OS X 10.5.8 "Leopard" isn't exactly straightforward either. You will first need to obtain a retail Snow Leopard DVD which Apple no longer sells, install it, then update it (that gives you the App Store), then finally upgrade to El Cap from the App Store. Your $200 budget needs review.