For the best finish I would recommend spraying the pieces disassembled. You can rent a sprayer from most sherwin Williams stores for ~$50/day.

I’d recommend starting with a primer made for wood and top coat using a trim/cabinet paint like sherwin Williams emerald urethane or proclassic. Normal wall paint will be susceptible to chipping and discoloration in areas you touch often.

If you don’t want to spray, I’d still recommend painting disassembled and use the smallest nap roller you can find.