I've never seen a wall mounted fan outside of a commercial building. Those I have seen were mounted about 3' below the 10'-12' ceilings and angled slightly downward. They were also in very large spaces, so the fans were quite large. Of course you can find wall mounted fans as small as 12", though 16" is probably a better size.

If your fan oscillates you have to make sure it won't bump into a wall or other obstruction, so make sure it will fit unobstructed before you attach it. A fan with a 90º oscillation might not work in a corner. For a screened porch I would mount it between two openings so it could pull in outside air.

Cost is probably the biggest issue. Most wall mounted fans cost between $40 and $60. You do need an outlet which could limit placement, or require installing a new outlet which would add to the cost. If you have an overhead light fixture you can put in a low profile ceiling fan with a light kit starting around $100. There will be chains hanging from the fixture to turn the light on/off and change the fan speed.

You should consider how all of these situations might affect how you place furniture in the room. After all, the fan will cool people best if it blows over them where they are seated.

Lots of good information to consider.