The scratch mitts are best for night time when they can really scratch themselves, and during the day let them explore and keep their nails short like tallg says :)

I only use natural products the first few months, so no baby oil for me. I used almond oil BP with a couple of drops of lavender essential oil. Ratio 2 tsps to 2 drops. If you don't want to use that I recommend Avene Trixera Cream. Expensive but very good.

Alcohol to swap the umbilical cord stump and keep it dry and clean.

Car Shades, especially with summer approaching!

Oh, and I ended up trying every diaper brand in the market before I settled for the one I liked. My advice is, try a small packet of each.........AND remember that as baby grows you should try different brands again, because the diaper companies lure you by giving you a really nice diaper a the very beginning, only to let you down with the next size up!