My current philosophy is to use a 4K monitor and fill the space you have with as much screen as possible. Consider the screen in that space to be your "canvas", upon which you will be displaying the game. The high resolution will allow for much flexibility by way of shaders or just appropriate sizing. Just because you have the screen real estate available, that doesn't mean you need to use it all for every title. As BadMouth stated, whatever you run will need to have similar graphical output flexibility to that which is available in MAME.
This also means, however, that you will want a decent system and a graphics card made within the last 10 years to drive the pixels. If you are using a 90's era Celeron with on-board graphics, find a nice 4:3 which fits, mount it horizontally and deal with the smaller vertical games...unless that is what you play mostly, in which case the opposite orientation would obviously be better. But this then becomes a niche build, as most other applications become size-limited by the orientation (if they support it at all).