I used to have the same set up, with me living in a seperate basement flat. I was provided towels though I ended buying my own as the ones provided were white and I worried about accidently dying them in the wash! I was provided with a sheet, duvet and cover, pillows and cases, TV though I didn't use it. Also wi-fi, as the flat was below the house so I used theirs as it was the same address.
Make sure they know where the electric box thingy and water stop is, how to work the heating, the guest thing is very important so that they know whether they could have guests. I was ok to have overnight guests, anyone really, as they trusted me with the children and so trusted my judgement.
The next job was also seperate but was over the road, I had to sort my own internet (trickier than you think as this was in France!). My boss gave me the code for their own wi-fi and let me come over in the evenings until mine was sorted. Again I was provided towels, bedding, even a flannel!
Both of these seperate-living jobs gave me all cooking stuff like a saucepan, plates and cutlery, glasses. One thing it may be worth checking if they need hangers, I had my stuff in suitcases for a week until I was able to get some!
Be specific regarding whether thay can go to theirs during the working day- both times for me, my bosses were more than happy for me to go home to grab something (coat if its raining, forgotten library card etc). They never said I couldn't take the children their for a longer period but I wouldn't want to, my home is my space and I don't want children bumbling round it! I certainly wouldn't go there to cook in the middle of the day unless I didn't have the children (occasionally the baby was in hospital for a few days so I would have the middle of the day off when elder siblings at school).
Let them know if there's a phone line, if you are providing a phone or expect them to do it. In one job I sorted it all myself, in the other they gave me a phone and told me where the phone line was but I would have had to have sorted it myself. Didn't bother! No need.
The food thing is more complicated- with all my live-in, in the house, jobs I've been told I can use any food I need whenever I need it, though I ended buying most of my own as I have different tastes. With seperate accomadation, you can provide food on duty but unless you want them in the house all the time something needs to be sorted. In the basement flat job, I had a food allowance of £20 a week, more than enough for all food off duty. That was 2 years ago. In the France job I wasn't given any and my contract stated I could only have one meal a day on duty anthing else would be a disciplinary matter (!) which meant I couldn't eat with the little boy and I had to provide my own breakfast on the days when I stayed over for babysitting.