If you are flying into London, you will not need a car. If, from London, you are going to Edinburgh, I would suggest flying as it both faster and cheaper than travel by car or train. You will have no problem renting a car at any of the airports in Scotland. All of the major rental companies (Avis, Budget, Alamo, etc.) are represented. If possible, pre-pay the rental in the USA as this will cost you less. My wife and I prefer to stay in country house hotels; the Scottish Tourist Board can provide a list of these. I would advise you to reserve your hotels before you leave. I can also recommend the Travelodge chain of motels/hotels as good value for the money (although they are bland and featureless). Again, if you book in advance you will save money on the cost of the room per night.

You can find 90% of what you need on-line.

I would advise you to avoid renting the smallest (ie cheapest) car as you will inevitably find that it is inadequate for your needs (you, your wife, your luggage). Likewise, I would not advise renting a car and driving to your hotel in London-- it's a waste of money and besides, you'll probably never get there. If you are starting you trip in London arrange to pick up your car at Stanstead Airport (north of London) it is easy to get to and you will avoid the hassle of the M-25.

Finally, get yourself an AA road atlas (available on-line) before you leave as this will be indispensable when actually planning your trip as it shows the locations of all sorts of useful things-- castles, monuments, rest stops, motels, etc.

Bon Voyage!