Tried most of the stuff mentioned above over the years - Nutrogena, Nivea, etc. None worked properly either making skin greasy, coming out when you sweat, having no effect or making dryness worse and causing skin to crack. Nutrogena was the biggest disappointment. It was quite expensive IIRC and promised so much but didn't really deliver. Hands felt greasy the whole time. And yes my hands went from being dry to developing a huge crack on my palm at the time depsite using lots of the stuff. Ugghhh! Nivea just made hands feel greasy.
So have now been using Vaseline Intensive Care Hand Cream - the pink stuff in the pink bottles for about 7 years. A little bit several times a day and at night. It's brilliant. No greasy feel or pungent aroma. Doesn't come out when your sweating away on the bike whatever the weather. Hands are supple and skin still looks youthful. Brilliant stuff.
For face just a light smear of Vaseline Petroleum Jelly including lips and nose, around eyes, cheeks and forehead. Great for lips. You only need a very small amount rubbed in otherwise you could look like a burns victim.