London Heathrow to Manchester by Train

You will find a lot of posts in the forum about this topic. Things that you
need to consider include where you are sitting in the plane, how much
luggage you might have to check, and your budget for that part of your trip.
At the end, though, the risk factor is whether your plane will be on time/early
or late, and no one knows that until the day of the trip. A second risk outside
your control is whether the E-passport gates at immigration will be working
the day you arrive.

Note that neither the Heathrow Express, Piccadilly or Elizabeth lines go directly
to Euston. If you take a taxi, that will eat up most if not all of the savings on the
train ticket.

After all that, my guess is that you should allow 3-4 hours from your nominal
landing time if you want to book a train ticket in advance.

There is a train every 20 minutes from London Euston to Manchester, so there is plenty of capacity.
That is not a problem.
As long as you are at Euston by 2.53 pm the maximum you will pay is £76.30.
That fare then starts again after 8.02 pm, until the last train at 10.03pm.
Hardly any of these trains call at Watford Junction so there is no point to taking the rail air bus to Watford Junction for a train.
If budget is tight buy a ticket on the 46 minutes past each hour train to Crewe, £40.20 until 3.46, £46.80 from 4.46 to 6.46, then £40.20 7.46 to last train at 9.46pm.
Then a Crewe to Manchester single. Full price is £17.40 single. But buy at Euston and there are always last minute advance train specific fares for around £5 to £7.

On a good day the Elizabeth Line/tube route to Euston takes 42 minutes. Heathrow Express then taxi would be about 5 to 10 minutes faster.

Due to flight uncertainties detailed above, it is too much of a lottery to buy a cheap train ticket ahead of time.