Is it slipping under load or just during normal pedalling or both. Does it slip on any of the other gears? normally when you replace a chain you are up for a cassette as well otherwise it slips/skips in certain gears, if the chain is replaced in time the theory is you wear out 2 chains before you replace the cassette. Considering you dont know the history of the bike you might be better off getting a new cassette and starting the cycle afresh, to your original question if you decide to purchase individual cogs(i wasnt aware you could do this although miche used sell them) then they must be ten speed shimano or sram, mtb or road no dif