Impossible to say how easy it is to find someone... it depends on where you live, what people in that area are wanting to work, salary, all sorts of things.
Advertise and see who you get applying.
I would need someone who could drive as we live quite rurally.
Take into account the costs of someone providing their own car. Offer to pay the max mileage allowance, so the nanny is more prepared to use their own car and maintain it to a good standard, have suitable insurance etc.
Max amount is currently 45p per mile.
How easy is it to find someone who would work 3pm-6pm 4 or 5 days a week.
It is not many hours and being in a rural location the number of people who may be wanting such work may be very limited. Consider someone who has their own young child perhaps, consider someone who lives close to you.
Rates in the local town are about £8ph gross, so I guess I would look around that level.
As the hours are low, I would offer more. You need to make the job attractive. Increase the hours a bit... if school finishes at 3pm, then nanny needs to start earlier to be at the school on time. Bumping the time a bit can make the job 16hours+ which may then appeal to someone who needs to work 16 hours or more to be able to claim Working Tax Credit.
If they have another income, or if you pay £111 or more per week, then you will need to register as an employer. See HMRC: Employers. Depending on the situation, you may not need to deduct employee income tax, ni, or pay employers NI, as the salary will be low.
Accounting software like BrightPay can produce payslips and submit pay info to HMRC, or you could write them manually and submit info via HMRC Online.