I have a 23 inch monitor at the moment and would like to get a second monitor. The thing is, I don't need a huge second monitor. I just need something to watch videos on while I do some thing on my main monitor. I've seen some vertical second monitor and think it would work great because I have limited desk space. I just don't know where to start! What size should I get, how should I mount it, etc. And of course it has to look cool!
I would just move your current monitor to the left and add another 23 incher to avoid problems with different resolutions, if you use the same size you can use it to game with dual monitors, assuming your gpu can handle that. A vertical monitor would be nice, but I find them hard to look at; screens are becoming wider and shorter because they are easier to view, our natural field of view is wide-screen, so... just take that into consideration.
I was looking for something similar. I wasn't able to find one that was cheaper than a regular 1080p monitor, and ended up dragging out an old 1280 x 1024 out of the garage and it's my itunes-steam chat-youtube monitor.
There's plenty of room on that desk for another 21"-23" monitor. I wouldn't recommend setting it up vertically if you mainly want to use it for videos. It's just a waste of pixels, and you essentially get a much smaller monitor with a much smaller resolution and huge black bars on the top and bottom. Get a 4:3 monitor if you're concerned about real estate.
Alternately, you could get a stand and another 23" monitor and arrange them vertically. That would be the best combination of viewing area and desk space, but it would of course be a bit pricier.
I have two 1080p 23" monitors, one in landscape and one in portrait. I use landscape ones for videos, games and viewing documentation or datasheets while coding and portrait one for IDEs and browsing the internet.