As a villa manager who looks after several holiday rental homes, this is the list we give to all property owners as minimum kitchen essentials. Hope you find this helpful.
Fridge with freezer
Microwave
Oven
Hob
Mineral water dispenser (may not be necessary where tap water is drinkable)
Toaster
Blender
Kettle
Coffee maker (either a Bodum type plunger or drip machine)
Tea pot
Water jug(s)
Water bottles
Plates, bowls, coffee/tea cups - minimum supply is one per maximum occupancy plus 50% (so 4 person occupancy = minimum 6 of each)
Water/beer/juice glasses (double maximum occupancy of property)
Wine glasses (double maximum occupancy of property)
Cutlery (double maximum opccupancy of property)
Chef's knife plus smaller paring knife
Can/bottle opener
Chopping board
Serving bowls x 2
Mixing bowl
2 saucepans
1 large frying pan or wok
1 small/medium frying pan
Chef's spoon and spatula set
Scissors
Oven gloves
Either baking pan or casserole dish
Set of plastic storage boxes (Tupperware or whatever)
Salt grinder
Pepper grinder
Milk jug
Sugar bowl
Other extras that are popular with guests:
Rice cooker
Kitchen scales
Children's (plastic) dining ware
Champagne glasses