Nanny of 15 years, mom of 2 with a nanny, and nanny agency owner here. I'm saying this all kindly to set realistic expectations.
Your best bet will be Facebook groups, neighborhood listservs, or care/sittercity.
You should provide a car and add them to your car insurance. You cannot reasonably expend a young adult who only works part time to have a car, fully up to reliability and safety standards.
You should plan to pay $30-35hr. You will not retain anyone for less.
Just prepare yourself to likely go through multiple candidates in a year. That way, if you do like most people do, you won't be surprised. If you end up retaining someone, you can be that much more happy about it.