trabot, here! Hello.
We have a house cleaner who has been in my life for years. She was with me before I was even married. Naturally she was thrilled when I had ds. I asked if she would be up to baby sit and she said yes. So at first I had her come over while I was home and kind of got the feel for her in this position. Then I went out for an hour or so on her next visit and did errands. Then slowly folded her in.
Now she is our number one choice when we need a sitter. I so trusted her and that was my number one consideration.
I'd start there or maybe your family's house cleaner, if they have one... and of course, any friends whom you trust, ask for referrals but above all, I would be home for the first visits so you can get a feel and explain how you do things.
by the way, DS LOVES her. He screams with joy when she comes over and he doesn't do that for any grandparent. but that's another thread....