There are a few considerations here. Not the least of which is how you are going to be feeling after your long overnight flight.
You experience may vary, but a few weeks ago the scenario for my travels was to leave the plane (we were near the front), walk for about 10 minutes, arrive as passport control ahead of most of my plane mates, get in line and snake through a maze, and finally use the e gates for passport control. My time in Passport control was probably about 10 minutes, but once again I was ahead of the others off the plane. Our checked bags were there, so we picked them up, walked through "nothing to declare." and we were ready to move on. I think that this was pretty much a "best case scenario" and it took about 25 minutes. I can see it easily taking an hour or more depending on how many other passengers are deplaning at the same time.
There was still a long walk to the train station from passport control. We had decided to use a combination of Heathrow Express and taxi for our purposes. This option is fairly easy and we bought our Heathrow express tickets for 5.5 pounds each in advance. We then took a taxi to our flat. Cheapest option? No.... Just what we needed after our long flights? We thought so.
There are several options and at least as many opinions about them on this forum. I encourage you to simply choose the one that feels right in terms of effort, cost, and time for your situation.