Staying right by London Paddington is probably a good option as well Heathrow express runs very early to late and goes straight into the terminals is only 15-20 minutes with proper places to store luggage.

I’ve stayed at one of the hotels just off Heathrow on Bath road and hotel Hoppa isn’t very reliable from my experience nor frequent enough and taking luggage on a normal public bus when there is no where to store it can be annoying for sure. Not an experience I will do again I would stay at one of the Terminal Airports or by London Paddington.

By London Paddington I would extremely recommend Norfolk towers very short walk away.