Diapers - in several sizes
Laundry detergent (Dreft) - there may be something new now that's better
Onesies (spelling:) - Can't have too many of them - in several sizes
Sleepers
Baby wipes
The cloth diapers make great burp cloths
Laundry basket -
I'd put all the stuff in a laundry basket and pack that in a big trash bag with a ribbon to close it.
If the budget is limited, go with the basics. Easy care.
These items may not get many OOHS and AAAHs at the shower, but practical is useful.