Really just concerned with footprint. Like, if I have to put a mid-tower somewhere near the TV, fine. But if I can squeeze it into the entertainment unit somehow, that's better.
That implies that the case is the first decision point.
I assume you have measured the available space.
Might be 2, 20, or 200 available cases that will fit in that space.
How do you sort out the ones that won't fit.....it's difficult without taking a lot of time and looking at each manufacturer's web site for each possible choice.
Amazon sorting is beyond pathetic. You can search for "13600K" and be shown toothpaste.
Newegg has generally excellent sorting, but I'm not at all sure they include dimensions.
The few cases that are shorter may in fact be considerable deeper, with the overall size in cubic inches still as much as an ordinary mid-tower.
Maybe depth is not an issue, but height is?
If you are the type that would frequently want to open the case for whatever reason, that might be a factor. You can tolerate certain deficiencies in case design if you only have to deal with them once....during the first assembly. Those defects may be intolerable if you want to get inside the case 3 or 4 times a year.
For a tower, case width below 8 inches will likely start to impinge on the cooler height. My case is 7 3/4 inches wide and I can't use a cooler taller than about 140 mm (5.5 inches).