You MUST do gross pay. You are the nanny's employer for this job As long as you agree a gross salary, and have a proper contract, then you are not responsible for her tax affairs from any other job she has.
I have a part time nanny (2 days a week). She has another job for the other 3 days. The jobs are entirely separate, both I and the other mum (whom I know) has agreed a gross salary and signed a separate contract with her regarding our own job. We don't need to know anything about each other's jobs, and we are not responsible for the nanny's tax affairs - just for paying the employer's tax and NI regarding our own job.
When interviewing, I was strongly guided by the rapport built between nanny and children. We hired the one who sat on the floor and played with the children, not the ones who sat on the sofa and ignored them while they chatted to us. However, I went through an agency so all the candidates were pre-vetted. Obviously you need to do very thorough reference checks / CRB checks yourself for any nanny you get through informal sources.
Be aware that employer's tax and NI (which you pay directly to HMRC every 3 months) is about 33% of the nanny's salary, on top of the salary you pay them. Also, you must pay holiday (our nanny gets 4 weeks a year, pro-rata), and decide what you are doing about sickness (our contract says SSP only, although our nanny is so infrequently ill that I top it up to full pay on the occasions that she is).
I expect there are sample contracts online, download one and go through it to make sure all the standard situations (holiday, sick pay, maternity etc) are covered.
Think about any boundaries you have that may not be universal (e.g. we had a rule about no TV) and make sure those are discussed at interview.
How will the flexibility thing (for an extra day a week) work if your nanny gets another job? That needs to be carefully discussed. Nannies may be very keen to get the job and say it is no problem, but once they've got your job, they will probably need to look for one to go alongside it.
We pay £8.50 gross per hour, but are in the north, so probably you'd need to pay more.
Do you need nanny to be able to drive? If you're in Oxford itself, you might not. We hired a non-driver, and I think she is especially loyal to our job because it would be harder for her to get another one (most would require driving).
Think about whether you want the nanny to be Ofsted registered. If you can get childcare vouchers from work, then she will need to be - you can offer to pay / part-pay for the process.
Also, check that your home insurance covers employer's liability. I think most do, but you have to inform them. That, I believe, covers you if the nanny injures herself in your house.
Also, think about whether you want the nanny to insure herself against your children being injured in her care - if so, you may need to offer to cover the premium - not that much IME. The advantage of that is that in the terrible and unlikely event of a life-altering accident to your child, then there would be a pot of money to help provide for their care.
You could also choose to go through a nanny payroll to make life easy for yourself. I use nannytax - expensive (i think I have to pay about £200 a year) but they make life blessedly simple and save me time.