It would help to see an example with recording & project parameters, but I believe the main problem you’re having here is called video judder.
That stuttering during pans is particularly noticeable when there are a lot of reference points in your video, no 1 clear focus point for your eye. There’s a lot of parameters that influence how strong the stuttering will be, but the main thing here is panning speed. The slower you go the better the results should be.
Higher framerate can also help with reducing judder. Comparing 30 to 60 fps – you could safely pan 2x faster in 60fps for example. Shutter speed is also a big factor – try matching it to the framerate.
You could do some post processing and add motion blur to help blend the judder, but that might also hinder your shots – depends. I wouldn’t recommend this approach though.
As for the vertical lines… the only vertical line artifacts I can think of would come from GPU driver problems. However, if you meant horizontal lines (interlacing) – that might be from “Field order” in project and/or render settings. Set Field order to “None (progressive scan)” and see if that helps.