I have had housekeepers for years. I finally stopped hiring single cleaners and hire a small local service. I got tired of handling the paperwork and taxes (you do plan on paying taxes to an individual, don't you?), and most of the individuals eventually found something else they liked better. A small service is deterministic - they do the same thing every time. I had to get used to it, and now I like it. As for trusting someone in my home, I don't leave valuables out much anyway. I have a small safe that keeps the jewelry, cash, and controlled drugs (I have some painkiller I use infrequently that might be attractive to someone). The silver and guns stay in a gun safe, fully locked and bolt to the wall (as is the little safe). This kind of basic protection is good for the girl who feeds my cat when we're gone and the plumber who I call. Housekeepers are the same. It doesn't mean I don't trust, but it makes my house less attractive to burglars too.
If if you have trust issues, you might have a better time with a single cleaner. Your friends like the one they recommend, so that's a good start. Some basic protection of valuables is just a good idea though, no matter whether you hire someone or not.