My first suggestion is pkgs of cloth diapers for cleaning up and burp cloths. They will last for a long time and I still use them for cleaning up spills.
When my second grandson was born he was a premie. In the neonatal unit they had little mitts to put on the hands but the mitts that they make are not small enough. I made mitts to put on the hands so he couldn't tear out the iv or the oxygen tube. Or scratch himself in the face etc. My daughter bought some receiving blankets and I cut them up and made mitts from them. If you want to do this just look at a slightly smaller than life doll to get an idea for size. They are just a clam shell shape sew two sides and sew the edge over so you can run a ribbon through to tie it on the hand. or you could use a little thin elastic.
I made some for my daughter's best friend's baby when he was born. They are easy to make.
No matter how big or little the baby they have a habit of scratching their face so these keep them safe.