Yeah, I'm a bad hub; I take over the dining room table sometimes. So the aforementioned TV option really doesn't work (and I already use a laptop for the computer), but thanks. I saw some nice table tablets but they were too expensive, a little too large, and I don't want a tablet unless I can run it like a laptop.

Any monitor with VESA mount. and that has the HDMI/DVI/Displayport and power connector on the bottom of the monitor, can be put flat on the desktop by removing the stand. Then, when you want to stand the monitor up, use one of those holders that is meant to hold recipe books upright.
But if you insist on a monitor that can lie nearly flat:
https://www.dell.com/en-us/work/sho...8ht/apd/210-alcs/monitors-monitor-accessories
The Microsoft surface studio 2 has a monitor that moves to a horizontal position.
https://www.microsoft.com/en-gb/p/surface-studio-2/8sbjxm0m58t4?activetab=pivotverviewtab