grooming + hygiene
Teeth & Gums: We used a Green Sprouts Practice Toothbrush that was great. Even though babies don't get teeth until 6-9 months, it's good practice to do brushing in advance (we do it every night as part of the bedtime routine) so they get used to having the toothbrush in their mouth and don't freak out when you try to start brushing later. The toothbrush is sort of like a chew toy for them that has some down-the-road oral hygiene benefits, and early brushing is supposed to be good for the gums as well. We also used these little finger brushes from time to time and found them helpful. I've also heard people like these gum wipes but I never tried them.
Nails: It can be terrifying to cut your baby's fingernails. A lot of moms just bite off baby fingernails at first, or use the file. Eventually you transition to real clippers and we have happily used these Safety First Clippers (there's a built in light, especially useful when clipping nails in the dark while the baby is sleeping), but don't get the Safety First scissors because they are cheap and basically worthless.
Hair: we have used this adorable Skip Hop brush and comb set from the newborn days through toddlerdom and it's holding up great, but it's been discontinued. The brush and comb in the set are basically the same as the ones in the Summer Infant set. Most brushes and combs are totally fine and will get the job done. The only thing I don't recommend are wooden combs -- the teeth are too thick to be effective, so even though they look cute, they basically don't work.
Sun: We relied primarily on physical shields (big sun hats, long sleeves), but in addition we tried several mineral-based sunscreens before we found ones that weren't too chunky, thick, etc. My top pick is Thinkbaby, followed by Coola, and I think all the other ones are basically the pits (Honest, for example).