National Rai is not a train company --It just displays the different trains running the route.

You can use National Rail or the trainline https://www.thetrainline.com to find trains - but the actual operator is Virgin out of Euston Station.

Everything you need to know about trains in Britain is here: https://www.seat61.com/UK-train-travel.htm

National Rail is a good place to start, and does combine all the timetables, but the train will actually be run by a company like Virgin or West Midlands. Yes, buying ahead will definitely save you money.

I almost always travel second class, first will get you a bit more room, and on a few trains might get you something more but not often.

Check if the senior railcard or two travel together schemes will save you (try dummy bookings to see the total out of pocket after adding the cost of the railcard

https://www.senior-railcard.co.uk
https://www.twotogether-railcard.co.uk

You don't need either card to book but you would need it once you are on the train - so you'd book in advance on line and then at Euston before boarding you'd go to the ticket window and purchase the railcard

Virgin Train
First class comes with access to a lounge at Euston station. Complimentary meals will also be served on board.

London Northwestern also serves this route, but I don't believe you would like to take this. The journey time is much longer.