Bath: get one of those lattice plastic clothe baskets and put it in the tub with a few inches of water in the tub. He can sit up in it. You can bathe him and it's bug enough to have fun in but he isn't wandering everywhere.

Clothes. Look for child clothes resale shops. They are everywhere. Prices are dirt cheap.

Food: probably formula since he is so young. Make per instructions on box. Test get on inner wrist. If it's uncomfortable for you it's too hot for baby

Diapers: costco

Bed: never every every have anything else in bed with a baby that young. No bumpers. No blankets. Sheet should be taught over mattress and taped down if needed. They make warm onesies. If he can escape swaddling no swaddling either. Basically nothing he can push into corner and suffocate against. A warm onesie is more than enough

Sleep: if he startles when you place him in a cold bed, pre warm with a heat pad. Do not leave pad in bed. Use it pre warm spot, then remove and lay baby down in warm spot. Be sure to turn off heat pad. Hot water bottle can be used to warm bed as well. Some babies sleep better with white noise. We used to leave the hairdryer on in the room just blowing air to get our son to bed.