Don't try and pay her net of tax. You must pay her fully salary, plus tax
And don't go down the cash-in-hand route either.
Both of these are tempting, the former especially for you - but if/when your nanny wants to apply for a mortgage she has to be able to prove her whole income. And HMRC do investigate.
Remember that she is your employee and, no matter how well you get on/how much the children love her, you must treat her with the same respect as an employee would have. She will have legal rights too, which you must make sure you're familiar with.
Definitely draw up a contract; if she's an experienced nanny she may already have one from previous employment that you could use as a start point.
An important thing to agree on is holiday - when she can take her holiday. You can't just assume that she will have holiday when you are.
Make it very clear, from day one, what you want her to, and especially what you don't want her to do. We had a nanny share at one point, and the other family were forever ticking the nanny off for things they didn't like, although they hadn't made any of those things clear!
A couple of examples where the nanny got into trouble:
- no pushing the pushchair along busy roads, because there would be too many emissions from cars at the child's eye-level.
- no processed foods to be eaten (but also with no definition of 'processed')
- no driving with the child on a motorway
etc, etc.
You may also want to consider what benefits you're prepared to offer the nanny. Sometimes these are more attractive than more cash - for example, we put her on our family gym membership, which meant not only could she take our DC swimming, but also she could put the baby into the creche for an hour while she went to the gym/had a swim.