I would like to know how you recommend that I travel from Heathrow Airport to Exeter University in the southwest. Is there a train you recommend? Are there several trains to choose from? If I am going to be there for less than a week is a rail pass relevant?
Coach is not a bad way to travel, I did it a few years back and I think it was about 3 hours and fairly reasonable price wise.
There are direct coaches from Heathrow Central that take about 4 hours - but they only run once every two hours. You can take a coach to Reading and a train from there to Exeter. This takes 3-3.5 hours, with a service at least once an hour.
If you use Heathrow Express to Paddington and change there to the First Great Western train (often to Penzance - yes, the Penzance of Pirates fame) for 2:02, calling only at Reading, and the full duration of the trip will be only 2:41.
It can be that quick as well using the coach via Reading - to some extent the fastest route involving rail depends on the specific terminal at Heathrow, which the OP hasn't stated.