I'd suggest that the train is the most effective and efficient option, from almost anywhere in London getting to an airport will be at least an hour's travelling, plus security time etc. and faffing at the other end, not necessarily worth it. Better off taking the train from London Euston Station and enjoying the 5 or so hour trip.
Train services are pretty good, despite the reputation. The London Euston to Glasgow services are Virgin trains only. Advance ticket purchases do reduce the price a lot and booking a seat is essential, or you might spend a lot of the trip standing up.
See link to get good deals on the trips:-
https://www.thetrainline.com/
or go straight to Virgintrains website.
I'd imagine the return, if booked soon would be about £100-110. Not too bad if you add the travel to the airport at each end to the plane ticket.
I think the sleepers are between London and Edinburgh or Fort William mainly on a Friday night.
If you want a car in Scotland to see a few things then rent one in Glasgow and go from there.
As C4S says driving on the other side is a bit different and its different again in Scotland; roads going north are often single lane in each direction with limited multilane sections and heavy speed monitoring. So travel speeds are slow. I drove back from Aviemore this summer in the 911...and between the sections with posted lists at 60mph but trucks at 50mph and few overtaking opportunities the multilane sections were welcome... with the average speed cameras making rapid progress challenging. (Thankfully I'd had a decent dose of open roads further north.......).
Renting a car in London or outside and driving up is an option, IF you have time to make it a journey in itself, stopping enroute to see things and even a night stop. The route either up the M1 or M40/M6 is likely to be unpredictable. In fact the M6 south of Manchester is a 50 mile long work zone with narrow lanes, variable speed limits and general buggeration. As a drive simply between the two places it is not a good one at all.
There are few nice A roads en route.....most are either east or west of the motorway and would be real diversions. North of Manchester you can drive your heart out on the moors but its a longish way off route. If you want to drive nice roads head north from Glasgow towards Fort William and then up Loch Ness on the east side... or head along the A9 for the views. Glen Coe is spectacular.
I'd suggest that whilst in London public transport is the best option.