We are not two countries yet - 2 nations (like states) but not two countries.
If you are concerned about your luggage think if the two of you can manipulate the two medium suitcases (what's medium, and how heavy are they) as well as the 2 carry ons without outside assistance.
Cound you carry them up a flight of stairs. You won't have to if you use the lifts, but there is often a decent step up into the train, and sometimes the station lifts break. There also (I don't remember) may be a couple of steps up into the th station but there will be ramps.
Do either of you have other limitations (this isn't true confessions, but for you to think about).
What will you do when you leave York? Train to London? Get a car? Be met by friends?