Starting in St. Andrews makes going north through Aberdeenshire makes some sense. Glamis, the home of the Queen's mother is a wonderful castle an hour from St. Andrews and just north of Dundee. I would then head west and connect with the A93 north. It will take you past Balmoral spend the night in Ballater. (Figure on a 2 hours.) Try to get up to Balmoral early so that you can stop at the Knock Gallery. There are great views from the garden of Balmoral and the countryside and a great gallery. From Ballater head to Inverness. On the way you drive right past Corgarff Castle--it beautifully situated in the hills. It's a tower house which was is very Scottish. It's under two hours to Inverness. You can stop at Culloden and then maybe a brief stop at Urquhart Castle. The views of Loch Ness are fantastic from Urquhart. Michelin's fast route takes you west along Loch Ness's north shore. Be sure to factor in time for pix. It's likely two hours to Kyle of Lochalsh and then another 45 minutes to Portree. Use ViaMichelin to plot your trip.
Here's an alternate route. This route still has you going to Glamis. I left it in, but you could take faster roads, the A91 to the M90 to the A9, but this route takes you up into the hills. You could skip Glamis and go to [Blair Castle]. It's about two hours to Blair Atholl from St. Andrews. This route also takes you through Dunked, very picturesque town square. Great place for lunch at the Taybank.
Check what is playing at the Festival Theatre to see if you want to stay in Pitlochry. Also, the Explorer's Garden is quite nice. I took a lot of pictures there. Also the Atholl Distillery is quite nice and photogenic as well. There are nice walks along the Tay, with nice back gardens.
I would drive down to Glasgow airport and ditch the car there. It's a pretty drive. Look into taking the Mallaig Ferry and south through Fort William, Glencoe, past Rannoch Moore and down the western shore of Loch Lomond. Figure on four hours at least with many many photo opps.