I suffer from extremely dry hands and cuticles, which also affects my nail growth. What do you recommend?

Using a good handcream and cuticle oil are essential.   An oil is better to treat extremely dry cuticles, as opposed to a cream, because it penetrates the skin more deeply.  A good way to intensify the effect of handcream and oil is to put gloves on top as the warmth generated will help the pores of the skin to open, and intensify the moisturisation - try this with washing up gloves while doing the dishes, or overnight with cotton gloves.  Try Sally Hansen 18 Hour Handcream and Diamond Strength Cuticle + Nail Oil.   Exfoliation is also very important as it sheds dead skin and helps boost circulation.  Try Sally Hansen Gel Cuticle Remover, to gently exfoliate dry flaky skin.