Shoes should be closed toe, usually black and easy to wipe clean. You're going to end up getting all sorts of things splashed down you, you don't want to be getting it on your feet and you don't want soes that will soak up whatever's been splashed, be it urine/vomit/blood/diarrhoea/other bodily fluid. You also want to protect your feet from anything landing on them.
It's worth spending a decent amount of money on something that's comfortable, you're going to be on your feet all day and cover a fair bit of distance, I work in one bedspace for 13 hours, my phone tells me I cover around 10000 steps in a shift, which is about five miles. I used to cover a lot more distance on the wards. As the other poster has said, clarks unloops seem to be really popular with the girls, I wear sketchers, they're shoe type ones with memoryfoam in the soles, they've over four years old now and I need some new shoes tbh, but they've lasted me well.