When you go into labor you should have some things packed for you as well such as nightgown, slippers, socks etc.
The hospital does provide gowns however it's best to bring your own because it will be more comfortable.
For baby you should bring, bottle, formula, diapers, wipes, receiving blanket and an outfit to bring your baby home in especially if it's cold outside.
Hospitals do provide some diapers but you will be charge a lot for them so it's best to bring your own diapers for your baby while in the hospital and for the baby to wear home.