Yeah definitely FreeCiv. There's also FreeOrion and obviously Wesnoth. If you want something with a tactical element you may want to try out UFO: Alien Invasion, which I've not played myself yet but hear good things about. Or if you're leaning towards management as well as strategy, get OpenTTD.

And as Pike says, check out GoG for some cheap classics, if your budget will stretch to a few bucks. Also remember sales are commonplace on there.