National Express Coach

According to the RS London 2014 book the National Express bus costs about half the price of the Gatwick Express train but takes up to 1-1/2 hours to get to that airport from Victoria station versus 1/2 hour by the Gatwick Express.

Taking the tube will take you about an hour, too, to get into the city. The advantage of train/tube over bus is that trains aren't affected by traffic. I have taken the National Express bus between airports several times, but I don't think that would be my choice to go into and out of the city.

From Heathrow the National Express coaches don't start there, but are on long-distance journeys from elsewhere towards London which can affect the timings. You don't state which terminal you are arriving in, which is an important factor on whether this mode is convenient.

Terminal 3, arriving at 6:20 a.m. On a Sunday. I don't know if the tube would be a better option since we'll have luggage.

Hi.
As above theres no National Express service from Heathrow to London.Nor do Megabus run thst route.
Unless you want a gold plated ride and fare on the Heathrow Express , Tube is the way to go.
For your Gatwick trip I would again choose train over bus, far less likely to have a delay problem

At that time Heathrow Central has 1-2 coaches an hour. Early Sunday maybe the claimed 50 minute journey time is maybe believable. Note the coaches are not not stop, there are intermediate stops at Earls Court and sometimes Hammersmith.

You do have the risk with the coach that if you miss your booked service you are accommodated on a space available basis on a later service and you have to pay an extra £5 and possibly an excess fare.

Last August I took the tube into London from Heathrow with a carryon bag and a tote bag. At that hour there will be no one there when you get on, so it's easy and there is plenty of room. I flew in on a Friday morning, so as the train proceeded into the city it got fuller and fuller with commuters, but that won't be a problem on a Sunday. I would do it that way again without hesitation.