Paint won't work; it can't penetrate the cement, so it just sits on the surface and abrades very easily; then it peels off.
I covered my basement floor with cement sealer; it's been about a year and so far it's holding up very well - which isn't too surprising, as the stuff I used (Behr) is intended to be used to seal garage floors, and hold up to cars. The Behr cement sealer is about $18/gallon, and I used two coats - but the second coat took less than half what the first coat did. It went on very easily with a roller, and my floor wasn't smooth - half of it was where I had pulled up loose linoleum, some was smooth cement, and some was the old linoleum that I didn't pry up - it's holding equally well on all surfaces, and cleans easily with water and vinegar. The down side is, I used gray (I think they had white, too) - but since I put puzzle mats down (work out space) I really didn't care a bout the color.