I did the exact same trip a few months ago and had a great time.
I had booked specific trains, but by luck rather than skill, somehow had bought an off-peak day return. i asked on this site when this ticket was valid, but as it was a Sunday, there were no restrictions.
I had booked a XCountry train but the train there was chock a block. Somebody was in my seat, so I just sat on another reserved seat. had I been asked to move I would have done, but I wasn't. There were folk standing everywhere, but luckily I had only a 10-minute journey to Durham. I returned on a TPE, a train company I had never been with before and had heard 'not so good' stories about, but it was perfect .. a pretty much empty train and very clean.
I am not even 5 % on the way to being an expert on tickets, but worth a look .. off peak day return. i booked through the Northern Rail website