The train ride on the east coast is very picturesque at the northern end, so it does have that going for it. If you book your train tickets ~3 months out when they go on sale, you can probably get an advanced purchase 1st class ticket for about the same as a virgin little red flight. East Coast first class is very nice, assuming virgin don't break it when they take it over in a few months...

Taking a virgin little red flight + tram/bus into the city is probably quicker and less hassle, but less interesting. Getting from Heathrow to Kings Cross to take the train to Edinburgh isn't too bad outside of rush hour - direct tube in just over an hour. Use your Oyster card for yourself, just top up some PAYG credit on arrival. If the others have suitable contactless credit/debit carsd, they can use those for the same price