Things needed for a 1 month old baby
I learned the hard way that simple is best! 1 month old babies don't need a lot to be comfortable.
Clothes - babies don't need a lot and they grow quickly so just a few items at a time is best. Your list should include a few onesies, some sleepers, a sleep sack or two.
I might be drawing a blank on the rest. Babies grow so quickly at that stage so don't bother yourself with a lot of clothes. Some things would be nice but aren't a necessity, like bottle warmers and wipe warmers.