I very lightly put it on my face, don’t get me wrong :). But it’s not a particularly greasy product.
As others have said, AHA (Alpha Hydroxy Acid) is a good way to exfoliate the skin and keep it looking young. Sunscreen is another factor - I know not many people put sunscreen on their hands, but it is a definite way to avoid the aging effects of the sun.
Alpha Hydrox is a drugstore brand that may have a good lotion to try. But check the label - not all their products actually contain AHA.
My favorite skincare company, Paula’s Choice does have a product specifically designed as an anti-aging hand cream. Personally, I just use the Paula’s Choice AHA lotion on my hands, followed by a regular moisturizer. But I guess this product eliminates a step, plus it has sunscreen.
What else would you suggest buying from there? It does seem like a cool shop. 
If you use a good moisturizer on your face, also use it on your neck and your hands. Personally I have to buy the primo stuff from the malls because nothing in the drug store keeps my dry skin from flaking off all day long. Estee Lauder is good, so is Clinique. But they are expensive.
A friend ordered a ton of stuff from them once heh. Off the top of my head, her favorites were this baby rash cream (which she uses for sunburns, but also very much for just VERY dry itchy skin). Rosebud Salve is good for dry cuticles, lips, etc. I’ve also heard good things about this hair treatment. Oh! And their perfumes are supposed to be great, too.