As a registered childminder myself, I show all parents who come to see me a portfolio containing all of my certificates, policies on how i deal with behaviour etc, activities i plan to do over the next few weeks, my working hours and rates etc. I also try to make the parents and children feel as welcome as possible and would encourage them to ask me any questions about anything (however trivial it may seem).
I would also ask them to come and see me again when other children i mind are with me so that they can see what we do and how the other children behave.
Do not be rushed into a decision, any childminder who genually cares about what they do understands that you need to be sure about them, we know how precious children are, most of us are mums ourselves.
Do not worry about your child being left with a 'stranger', because you should make as many visits as possible to the childminders and get to know them before leaving your child full time, (build up the time you leave them bit by bit when ever possible), i have never looked after a child yet who has not settled after about the third visit.
I would also only agree your first contract for 4 weeks, then if you or your child is not happy with the childminder, you are free to not renew it, but if you are happy you can renew for a longer period.
I think you instinctively know if the childminder is right for you, i have always had an instant rapport with the parents and children i have childminded and all of the mums (and some of the dads) have become good friends.
I hope this helps and good luck.