So I kind-a got flamed for what I "offered" to pay when I was looking a few months ago.
I learned a few things.. you should pay what they are willing to take (in consideration for what you can afford too). I also used a web site care.com (a fellow diser rec) to find her, and had 30 applications in like 1 -2 days. I WAS floored and overwhelmed, as I had always used craigslist. (successfully too).
I pay a full day (7:45-6) at 55$ a day. I also pay her 10$ an hour for any O-T so if she stays until 6:30 or 7 I pay her 10$, sometimes I am sched on a sat, or a date night.. and I pay her either 10$ per hour, or at least 60$ if it is more than 6 hours on a sat like 8 I still give her 60$. SHE IS THRILLED with about 300$ per week take home. I AM THRIIIILLLLED to have her. I am in MI.
This is slightly different that what you are looking for in hours, so the fewer hours you give, the more $$ per hour I think would end up being fair. I would think 5$-6$ an hour and make it a per day, (as long as it was full time) even if she/he leaves early.. IE if she works 3-10 or 3-9 make it 50$.. and then a fair wage for over nights too maybe 10- 6 also is 50$ really depends on the amount of hours. If you are doing 3 hours 5 days a week and 1 over night I think 8-10$ an hour is what you will end up with.