As a veteran of many SC holidays over the years:
While you don't need a wide range of tools in the kitchen, you do need functional basics.
1 decent small sharp knife, 1 bread knife, 1 decent larger sharp knife.
1, preferably 2 wooden spoons.
Veg peeler that works, tin opener, corkscrew
Ladle, serving spoon, whisk, spatula/egg turner
Proper pots - with lids - to suit the size of group that you are marketing the house for. So yes a couple of small ones but at least 1 large one for enough rice/pasta if all beds were occupied by adults, and 1 large enough for sauce to accompany that. At least 1 decent pan (large enough), preferably 2 (in which case, 1 should be small and the other fairly large).
Trays for the oven - at least 2 - a roasting tin with decent lip, and tray that can do cookies or kievs or oven chips etc
At least 1 decent sized bowl that can be used to mix things, serve things to the table (hot or cold) - and it would be great if that could also go in the oven to cook but latter is a bonus
OVEN GLOVES!
Also, 2 tea towels and a hand towel for the kitchen (a few more teatowels if no dishwasher)
Drying rack for washed dishes, and a washup brush
Crockery:
Enough knives, forks, large spoons, small spoons for each bed (we've been in houses ostensibly holding 8 adults with 4 forks and 2 teaspoons...)
For each bed place, there needs to be:
1 dinner plate, 1 side plate, 1 bowl, 1 MUG (not wee cups and saucers!), 1 juice glass, 1 (proper - not thimble sized) wine glass, 1 straight glass (for water, beer, squash etc - could combine water and juice functions if using larger glasses, but not using smaller ones)
1 extra set, or a few extra bowls, or cups and saucers as well as mugs, are all added bonuses
Milk jug, sugar bowl, tea pot (coffee plunger), salt and pepper pots/mills
Preferably 2 milk jugs (1 being decently large) or a gravy jug for serving sauces/dressings, also a water jug is great but a bonus
Extra set of crockery (already mentioned) or some extra serving dishes, a couple of ramekins for smaller items would be good too
Appliances:
Kettle
Toaster
Decent cooker with grill and oven functions and that the hob actually works well (lots have these pads that take forever to heat up and then to cool down so are very hard to cook on)
Microwave
Dishwasher is great to have, especially if there are not spare sets of crockery (so you need to wash everything after breakfast to have lunch or even mid-morning coffee and cake etc)
Washing machine and dryer or combo are very useful, especially with kids
In a hot press/cleaning cupboard:
Hoover (and a spare bag/make sure bag is not full)
Dustpan/brush, full sized brush, mop and bucket - you hope to never need these, but it's very useful to be able to find them if you do
Maybe not your full cleaning supplies, but a bottle of cleaning spray and a cloth
1 spare set of sheets for each size of bed - so 1 double and 1 single, and 1 cot sheet, not 1 for every bed in the house - just in case they need to change and wash sheets midweek
Beds with decent sheets, duvets suited to the house and season (so an older house with poor insulation and used in winter needs to have heavier duvets, but well insulated and heated house for a warm summer needs lighter ones)
Something else to throw on the bed if some guests are cold - blanket, fleece blanket, spare duvet etc -
1 pillow per person, but at least 1 spare pillow per room
(No - I am not trying to make the house great for extra guests without beds - this is about comfort of those beds - we usually have houses sleeping 6 for just 3 of us and use all the pillows and most duvets just to keep ourselves comfortable).
Also in bedrooms, some kind of lamp beside each bed/each side of doubles, that can be reached from in bed - on a shelf or locker to also put keys/phone/book
As well as socket for lamp, other sockets accessible for charging phones beside bed
1 mirror in each bedroom - with at least 1 full length mirror somewhere in the house
Space near each bedroom mirror for toiletries (dressing table/shelf etc), and a socket for hairdryer etc
(A hairdryer is useful, but I tend to bring my own decent one as SC ones tend to be travel or very low speed types - but I need a socket, and there are lots who also want straighteners/tongs etc as well)
Bin of some sort
Bathroom
Shower with decent pressure and hot water, and not the head encrusted with limescale so all the water runs down the hose rather than out over the person
At least 1 decently large and 1 small towel per bedroom (not 1 hand towel and 2 weeny bathtowels in total for a house sleeping 8)
Towel type bath mats that are changed/washed with each turnover - not a scraggy carpet type that sits there for years
Space to put toiletries/washbags
Hook on back of door for clothes while showering
Non-slip bath mat
Mirror
Bin with a lid
Dining table with enough space and enough chairs for the number of beds.
Enough comfortable chairs in sitting room for number of beds
Bookshelf can be useful - tourist info on local area, couple of kids books, couple of reading books - spend £10 in a charity shop to fill it if you don't have any at home to get rid of
Also, a deck of cards and couple of board games can be good (again, second hand is fine) - but check periodically that all parts/cards are still there
TV
A few lamps around the room so it's not just the central light
If targetting families with small DCs, make sure the equipment is functional - cot is sturdy, high chair can be used easily and either has a tray or can be pulled into the table etc. A step in the bathroom to reach the sink/toilet can be great. (Ikea stuff is all perfect for this - no need to spend loads in Mammas and Pappas - just be functional, and easy for guests to clean during their stay and you to clean between stays).
Wifi would be great to have nowadays - people can stream their own services
But we've stayed in some with old VCRs or DVD players and a few tapes/discs to play which have been good on a rainy day.
Outside, having a table and chairs is great.
A BBQ is handy, or else a space properly set up for the 1 use BBQ trays. (A few key tools - tongs, spatula, fork - for BBQ would also be good to have)
Also stayed in a few with a picnic blanket and plastic crockery for picnics in a tote bag which was great for us. And a bag of buckets/spades/sand moulds was great in another near the beach.
Consumables are handy, but not essential.
So I always like to see at least 1 extra toilet roll per bathroom on arrival, but always assume I need to restock that myself (a few have had plenty for the week).
1 roll of kitchen towel on arrival (not necessarily a full roll, but at least half a roll, not just the last few sheets) is great to have
Tin foil and cling film also
Items like bamboo skewers (especially if there's a BBQ) can be great
Some washing up liquid, a handful each of dishwasher tablets and washing powder tablets would be great to have.
I'd also budget a cheap supermarket scrubbie pad for each turnover as well, and a j cloth -
And a bottle of liquid soap in each bathroom - whether it is in a bought dispenser or just a shop bottle of soap is less relevant than being able to see into it (and if you do water it down, only do that a little - not so much that it is vaugely soapy water coming out, and the same with washing up liquid - cheap and cheerful refills are fine, just not totally watered down ekeing out).