I think the 32" would be too big to rotate, since you have so much screen size, vertical games would probably be big enough with that screen turned horizontal.
However, as far as I know, a screen that big has not been tried yet, so I personally would love to see that being done.
However, the 22" and 19" screens would be very good candidates.
But a word of advice, test the screens in vertical orientation before you commit to using them.
Hook them to a PC with mame, set mame to rotate the view for vertical games, then turn your screen vertically and see how it looks.
Things to look for is viewing angles.
With a game running in vertical, and the screen physically turned vertical, move left to right of the screen and see if the screen view becomes messed up.
LCD monitors have maximum view angles. Some are not over 20-30 degrees. In other words, if you are viewing the screen dead on in the center, then you move left or right and up and down, when you have reached the max view angle the screen will drastically change.
Most lcd monitors have a wide view angle left and right, but not so up and down.
And when the monitor is rotated vertical, up and down become left and right to the viewer. So be sure to check left, right, and up and down.
I always look up the specs on a monitor before I buy it, just to make sure it has very wide view angles up and down, if I intend to rotate it.
Good luck with your project, and please keep us informed as to what you do with the rotating screen.