Hi. Welcome to the habit.

I would say, if you're using a CRT monitor, you probably want to avoid rotating - that's tough to rig up with a heavy CRT plus you have to worry about degaussing. People have done rotating CRTs so if you feel up to it you could give it a shot, but I know I wouldn't want to.
As for size, if you're not planning on rotating, the bigger the better. But you'll probably be limited if you're planning on a computer CRT. I think anything bigger than a 21 inch (probably about a 19 inch viewing area) is rare, and if you do find one, it may not be cheap because of the rarity.
If you're wanting it mainly for vertical games and there are only a few horizontal that you really like, I'd say mount vertically and live with the small screen size for horizontal games. If you feel you need a big screen size for each orientation, I'd say you're best options are:
1. Use a CRT television of at least 25 inches (a computer monitor is fine too of course, but you're unlikely to find one that big for cheaper than a TV if you even find one at all) and mount horizontally. Horizontal games will be pretty big, and vertical games will be about the size most of them were in the arcade.
2. Use a computer LCD monitor and rotate.
I did the second option, using a 22 inch 16:10 LCD (pillarboxed to 4:3 that's about 19.5 inches - oh yeah, gotta have the proper aspect ratio!) mounted to a lazy susan with a rope coming out the back of the cab to rotate. It works very well. I'd show you pics but I don't have any and my cab is disassembled at the moment. This is a great solution for having a good screen size on both orientations without having a huge monitor, but I'm actually considering just mounting it in the vertical orientation when I rebuild my cab since that is mostly what I play anyway. As neat as a rotating monitor is, I find being able to rotate the monitor takes away a bit of the feeling of it being a real arcade machine. And it takes away a bit from asthetics too - in the vert orientation, you have to have some empty black space on the sides between the monitor and the bezel, and in the horiz orientation, you have to have space on the top and bottom in order to accomodate both orientations.
Anyway, I figure I've given you some stuff to think about. Good luck!
