There is probably no best agency... different people will have a different experience of each agency.
For a list of agencies, use the SCSWIS Care Service Search - select Child Care Agency as the service type.
How much can you afford? Work out what budget you have, then back out the costs, ending with what salary you can offer. Keep in mind you will have costs such as:
Activities, Mileage whilst on duty (if nanny uses their own car), food/drink, Employers National Insurance, Employers Liability Insurance (check your home contents insurance policy, you may find it is already included), Payroll Admin (I do suggest you use a payroll agency at least for year1, so you need not get too involved with the monthly payroll run and end of year reporting. PAYEforNannies have been doing my payroll for nearly 5 years, so I suggest contacting them.
For an example of costing, see this calculation I did for a 3 day a week nanny, as that will show some of the costs to think about.
To get a feel for Employers NI, use the excellent UK PAYE Calculator (2013-14) created by MrAnchovy who posts on this forum. I have linked to the 2013-14 tax year version of the calculator as you may be wanting a nanny top start after 6th April 2013. If you need them to start before that, the taxation costs will be different. Use the calculator as a guide, the payroll service will do the monthly calculations and produce the payslip and tell you how much to save for paying to HMRC and when/how to pay it to HMRC.
Agree a GROSS wage with your nanny. Nannies are no different to other employees, so should really understand gross wages... we are no longer in Victorian era.
Agency - do you need to use one? If claiming Tax Credits then you do need to use one in Scotland but if not claiming, then you can self recruit if you wish.
Qualifications - whatever you like if you are recruiting yourself. Consider what qualities you desire, it's more about the person and their life experience I feel than it is about their qualifications.
Tips:
Look through the many message threads on here about nannies. Use the Advanced Search to find them. Try using keyword nanny and limit the search to this section of Mumsnet. Example: messages from the past couple of months. Tip: restrict the search date range further to get all the messages posted in a particular timeframe, as search is limited to 500 results.
Think about what you want a nanny to do, make a list of the things. Then from that list, create a job description.