There are several commercial hand cleaners that work well with GoJo being one of the most well known brands.

For grease and casual dirt I've found hand dishwashing soap to be very effective. I keep a squirt bottle of it in the laundry room so I can get my hands clean before going into the rest of the house.

For latex paint, the best remover is speed. Wash it off before it dries. For oil based or spray can paint or lacquers, acetone is a good remover.