Quality of the NHS in Scotland?

The NHS Scotland is a great service and you'll find that the waiting times and appointment delays are generally much shorter than what you find in England. Once you're settled in your accommodation in Edinburgh you'll need to register with a GP in your area. There's a list provided here if you don't see one in passing - Nhs24.co.uk. For the documents you'll need to bring with you have a look at the Expat Arrivals Healthcare in Edinburgh page. After you do this you'll be assigned an NHS number and then you can make appointments as needed.

If you're coming from the States you may find that medical care in Scotland is less luxurious and not as comfortable as the private facilities you're used to in the US, but nonetheless, the care is good and the doctors well-trained. There are of course bad experiences to be had - just like in any situation - but you must just assert your needs and insist on what you need.