you got a lot of suggestions already.
For actually finding a babysitter.... there is a website which I have heard good reviews about: www.care.com
You can actually see/read about the providers... and they are supposed to be background checked too.
I see nothing wrong with asking questions from a list.... as a PART of a conversation.
To a certain extent, a Babysitter will accommodate the wishes of the parents... regarding their kids. A babysitter will either be rigid, or flexible.
So YOU decide what you want.
And, go by your instincts as well.... gut instinct, is often correct.
YOU decide if the Babysitter is "allowed" to take the kids out. If she does, under your approval... then she has to have insurance, liability insurance, you should sign an "approval for transportation" letter, which she as a Babysitter should have templates for. She also has to have car-seats in her car... which YOU provide etc.
Also keep in mind, that if a Babysitter feels micro-managed... they will probably get turned off... especially a seasoned babysitter. So, although YOU determine what is done with your kids... and how... and what philosophy of childcare you want... you also have to trust your Babysitter.
I used to Babysit. I stated my philosophy of care to the clients... I also accommodated parental wishes. I was not however, someone who was expected to "fix" their child. If you know what I mean.
Also, know the difference between a Babysitter.. and a Nanny... and a Nanny that also does household things. As a Babysitter... they should not be expected to clean up your house for example. The primary role, is babysitting... so you/your wife, has to decide what the primary role is, for your Babysitter.
All the best,
Susan