We used to travel up and back from London to Edinburgh on the sleeper, but this has now become as expensive as a decent hotel! I second flying into Glasgow Intl or Glasgow Prestwick or Edinburgh. You can pick up a rental car and easily make Stirling in two hours, check into your B&B or hotel, and be more-or-less fresh as a daisy in the morning. Book your rental car in advance and pre-pay the rental as this will result in a significant savings. Likewise buy your gas/petrol up front and you won't have to worry about returning the car with a full tank.

As far as driving up from London goes, I have never made the journey in much under nine hours. London to Edinburgh is about 450 miles and even though you can do a theoretical 70 miles per hour the whole way, my experience has been that it's really hard to average 50-60mph, and that's sticking to the motorway.

If you fly into London, allow 2-2 1/2 hours to get from the airport to your train station; I've done it in less, but inevitably it takes at least an hour and often more. Time of day, day of week, and possible strikes, can seriously delay things.

Other than that, enjoy your trip.