We just returned from a week s/c and we feel these points as important:
Clean and tidy, fairly modern, no casts of but purposely furnished/set up
Enough towels, loo paper, kitchen towels, starter set for washing up, hand soap, bit of basic cooking ingredients like salt, pepper, oil, ketchup, sugar, tea or coffee,
Enough mugs, cutlery, plates to last more than one meal
Decent pans and pots
Instructions how to operate complex TV set ups, where laundry facilities are if not in the house, heating (especially if the landlord is not on the grounds)
WiFi, especially if there is no mobile network, more than one code or a general password
Depending on the garden, bbq, nice simple garden furnitures, maybe a trampoline
Have items for children available but maybe not as constant, provide if requested like cot, high chair, sand toys
I like a bit of welcome gifts but I am not fussed if there is nothing. We do a biggish shop on the way to the cottage anyway.
Our cottage said we can use online shopping with Tesco and the address is recognised.