I'm with Mardee here. Don't be too ambitious in your plans, especially if you are planning to spend any time in London and Edinburgh/Glasgow. You want want/need a car in any of these places. However, once in the Highlands, a car could be an advantage, depending on where you plan to stay and what you want to do/see. Remember distances may not look far on a map but will take a lot longer to cover than you might expect. Driving in Scotland is slow. Build in time to stop and enjoy the different places.
Any of the places you mention would make a good base for a few nights. Aviemore and Ballater are more in the Highlands. Aviemore may be better if using public transport.
You have plenty of time to think about this and September/October will be a lot quieter too. Pressure on accommodation will be less, although places like Syke still book up well in advance.
The Secret Scotland website has ideas for different lengths of self drive itineraries and will give an idea of what you clould do.
What not to miss ?
That's a difficult one as my 'must see' list could be the list from hell for you! What sort of things are you wanting to do see - ruined castles and abbeys, stately homes, scenery, walking, museums and culture, sporting type activities, high adrenaline stuff, shopping.... the list is endless. Any good guide book will give you a tick list of popular ideas.
My favourite is DK Eyewitness which has lots of pictures and covers many areas not in the other guide books. The maps are also good enough for initial planning. They do a guide to Great Britain as well as one just covering Scotland. You can buy a cheap second hand copy from Amazon - the basic information won't change much but do check latest opening times on the web.