Sometimes old fashioned is the best. I just bought a Fuller string mop for my hard surface floors. As advertised, this mop catches the dirt and cleans off easily. I use a string mop, but this one is built to last with all metal parts, and a sturdy mop head with tough non-shedding twisted string. The entire mop is about $14.00, and the mop head is replaceable.
More about the Fuller Brush Company, established in 1906.