I'm actually ok with a one player CP. I will be building a 2 player cabinet for horizontal games (much larger) but I wanted just a small 1 player cabinet, narrow as possible.
If you want a narrow cabinet, then examine mini cabinets, or an Atari Assault. Actually, the Assault only LOOKS narrow, it does have a full sized base at the bottom, which means it is still 24" wide, but the rest of the cabinet is only like 18".
Also, 90s style cabinets are the big ones (as are 70s style ones oddly enough, but not as big as the 90s ones). The smaller cabinets are the early 80s ones.
The vast majority of cabinets will take a monitor in either orientation. Exceptions include, Assault, many cocktail tables (especially those Atari ones that offset the vertical monitor to one side, and also those twin monitor nintendo ones), a few oddball minis, and most moving cockpit games (which obviously wouldn't be your first choice for a vertical cabinet).
If you are building one yourself, just follow plans for any of the standard 80s style cabinets, and reduce the width by 5 inches (measure your monitor first to fine tune that total, as my Assault was roughly 5 or 6 inches narrower than stock, and the monitor just barely fit, it was obviousy designed to be only as wide as the monitor).