Heathrow to Plymouth- coach or rail?

One other consideration: how much luggage will you have? Your luggage will be stowed for you under the coach, but you have to completely manage carrying your own luggage with the train.

Good point about luggage. No checked luggage on flight. One rolling bag, one smaller bag.

Or you could get the RailAir coach to Reading and get on the Plymouth train there if you don’t want to go into Paddington first.

For me, absolutely the coach.
It is straight there from Heathrow Central Bus Station at Terminals 2 and 3, maybe 2 hours longer than the train.
If you're on either of the two direct AA flights you arrive at T3
Coach tickets are £25 each way, amendable.
The train is £12 each way into Paddington on the Elizabeth Line (you've already missed the cheap HEX fares), then £38 each way if you're lucky Paddington to Plymouth, more likely closer to £60, non amendable. So if there are issues with your flight your train ticket has gone. And no-one knows until 14 days beforehand what is happening with rail strikes.
You can book the Coach now.
National Express are not remotely like Greyhound. Very modern, comfortable coaches, USB ports and WiFi. The seats are far better than on GWR trains IMHO. The coach has a restroom.
Both Heathrow and Plymouth coach stations are very modern, safe places, with full time security.
Register for a free account with NatEx and you avoid the booking fee.
You don't have to pick a particular seat, everyone gets a seat (unlike on the trains). But if you want to spend the extra few pounds choose Seat 2A if you can- front seat, nearside- you get unlimited leg room.

Thank you to the reply from the Lake District. I will look into this further. £25 is a fantastic fare. I don’t know that the two hours is material; I’ll very likely be sleeping!

Thanks all for your advice! Lots to consider. Always glad to hear from folks who travel and/or who live near my destination.