Scotland is different to England in respect of childcare registration, in particular home childcarers (nannies).
Starting from the last question in your post, to use Childcare Vouchers you need to hire the nanny via a registered agency.
This mumsnet post from 2009 has some discussion about fees involved - one off fee is mentioned, a monthly fee is mentioned.
The agency must be registered with SCSWIS - Find a Child Care Agency (if the type of service box is not showing Child Care Agency, select that from the dropdown list.) Enter in your postcode and select a mileage, say 50 miles then narrow it down a bit from there if you have several agencies in your area.
Looking at the list I got from a test search, not all seem to be Nanny Agencies. Some offer Sitter services, Mobile Creche, Temporary staff to Nurseries. So I would suggest you get an initial list of agencies then look up on their websites, or call them, to find out if they provide nannies. Then talk to them about the fees involved, including if say you were to find a nanny yourself could they then put that nanny through the agency for childcare voucher purposes.
Childcare.co.uk shows a figure that the individual nanny has entered into the system. That figure may or may not be for nannying work, it may be for evening babysitting. You also don't know for sure if the figure is Gross (before tax deductions), or Net (after taxation deductions). So I would suggest you treat the figure as an indication but to be aware that until you contact them and discuss the childcare you actually need, the salary you would need to offer that candidate may differ from the figure on the website. The figure given may also be for all-day care... so contracting to say 50 hours a week, not for part-time care.
As the employer you will decide what salary you will be paying someone to do the job. So now you have a rough idea of what people in your area may be expecting to be paid, calculate what you are actually able to afford to pay and what you expect them to do for that salary. Try to keep in mind as many of the costs involved as possible, for example... if a nanny is collecting children from school - how are they going to do that? Their own car? If so, then there will be mileage payments to take into account. HMRC: Approved Mileage Rates
Look at the cost of employing someone, such how much Employers NI would be paid by you, on top of the nannies Gross salary? Use the excellent PAYE (2012/13 tax year) calculator by MrAnchovy. That calculator will also do Net to Gross calculation, though you will need to know the nannies tax code. Use code BR to see the worst case situation - code BR will represent all income being taxed, instead of taking account of personal tax allowance.
DS also starts school the day after I start my course!)
So what happens on the day you start your course? DS would need fulltime care, not 3pm-6pm. Same problem will occur on any days that school for whatever reason is closed, yet you are at college or on placement (do you do placements as part of PGCE?). What about school holidays - you may or may not have the same holidays as your children. What about minor child illness - school does not want them to attend but they are not really that sick, so can you justify missing college?
Think about what backup childcare you have available, as if you hire a nanny for after-school care only, then that nanny may or may not be available to do all day care when it's needed.
Read lots of this section of Mumsnet. There have been quite a lot of discussion over the years about things like Contracts, managing an employee, examples of what nannies do during their working day and what some nannies won't do.
You can use Mumsnet Advanced Search to limit a keyword search to this specific part of Mumsnet Talk (select Choose Topics, then from the list that appears, select "Childminders, Nannies, Au-Pairs etc" in the left column and click the purple > button to move that to the right column. Then click Save Favourites. Check that you have a keyword (or words) entered in the box below where it says "include the words:" and click on the purple Search button near the bottom of that form. Sounds complex but it's easy once you get used to it. 