MrsL I have used the website Vrbo.com quite a bit for villas, apartments, condos around the world with excellent success.
I'm not sure of the offering of catered villas bur I am sure they exist.
I did know of one place in Tuscany that a friend stayed at that was more of a b and b style villa ( ie the owners lived on site). I have it saved on my bookmarks on another computer so can dig it out for you when I remember.