Going south (when the worst of the shaking was) I was in coach B, seat 70 (that was an 801) and returning I was in coach G seat 27 (Class 800) - both 9 car sets. There was a bit of shaking on the 800 but no where near as bad. Here's some screenshots of the seating plan on LNER's 800/801s I found on the DPSim website:
You must have been sitting directly above a bogie, I was sitting in a seat above one on a recent journey and I made the fatal error of ordering a cup of tea from the trolley. It was sloshing all over the place every time we went over points or encountered any bump in the track. By the time it had cooled down enough for me to drink it around a fifth of it must have poured onto the table or floor. Always try and get a seat in the middle of the carriage. It's still far from the best ride quality in Britain but it's at least stable.
I didn't really have a choice, I just said I want to sit next to a window facing forwards and it foist the seat upon me (I booked through the TPE site)
Some websites let you choose the seats yourself. I'm pretty sure Trainsplit does. I'm not sure any TOC websites do though. I know for a fact GWR and CrossCountry don't as I tried booking with them recently and they just had me choose my preferences.