Avoid getting confused between Employment Law and Tax Rules.
Your relationship with your nanny will be that of an Employer:Employee, you will be wanting to dictate when they do the work, where they do the work and how they do the work. You probably don't want a situation where you need childcare at say 8am but they say they can't come in until 10am.
So they are your employee, they are not self employed - for the purposes of Employment Law.
PAYE has to be operated if you pay £107 or more a week, OR if they have another job.
So, find out if they have another job. P46 is the HMRC Form that is used for confirming if the employee has another job or not. This PDF is now a digital document, so you need the latest version of Adobe Reader to view this form.
If they just tell you that they don't have another job... then at some point get them to complete a P46 anyway, so you have on file that they told you that you were their only employer.
Agree a GROSS salary, regardless of the tax situation. The situation over them having another job could change at a future time, or they may have deductions from income, or something like that which is done via taxcode, so protect yourself from such costs by agreeing a Gross salary (the salary from which deductions are made) rather than Net (the salary after deductions have been made).
Salary to offer is hard to know. Decide what you feel the job is worth to you, then offer the salary and see if it's worth it to them to do the job for that amount. You need to offer at least National Minimum Wage (which varies depending on their age). Maybe compare it to other jobs in the area... I've just seen a part-time admin assistant job in Wareham advertised at 7.56 and hour. Would nannying compare to that, hard to say, but it may help you to decide that £8 an hour is a suitable rate, rather than say £10 an hour.