Does it matter whether I take Virgin Train or GNER between the two cities? Is one better than the other? Is first class worth the extra money for a mid-morning weekday trip?

GNER trains will have come from London, Virgin trains will probably have come from the South West of England on slower tracks therefore they COULD be delayed sometimes substantially

If booked on the GNER website, specically GNER tickets are 10% cheaper

For a 2h30m trip I wouldn't be bothered with 1st Class, i'd be more concerned about getting seats on the right hand side of the train so you can admire Durham Cathedral & the Northumberland Coast.

There are several "fast" trains that go from York to Edinburgh. In England fast means fewer stops.

A few years ago I took the Flying Scotsman from London to Edinburgh. There were only 3-4 stops, including York and Newcastle. The east coast of England is very pretty.

I've ridden this train route frequently and there is a world of difference between classes: second class(standard class)is typically sardine city crowded (be sure to reserve), lots of litter, tiny seats, whilst first class is amongst the finest first class in Europe - with free beverages and snacks served at your seat and always empty seats - no need to reserve so you can just show up at the train station. If arthritic certainly go first class if you want to get into and out of your seat.
But first class is so pricey i'm not saying go that way but there is a world of difference on this and all long-distance UK trains i've been on.

Thanks all. I'll use GNER and try to get a discount 1st Class ticket.