If you want to mine sha256 based coins, a used S3 might be a cheap start, but as others have said ROI is hard to get these days.
You could get a Compac USB stick or two and solo mine for fun.
With S3, there is not ROI at all. The cost of electricity will be higher than the bitcoin produced if you pay for electricity.
I did preface that will "ROI is difficult", which it is. Those of us on municipal electricity with very low rates can. But yeah, unless you solo mine and get incredibly lucky very early, these are not money makers right now. If BTC goes WAY up, then that's a different ballgame. Never say never.