Window or wall mount
The differance between a window and wall mounted A/C is the mounting system.
Window units are usually smaller BTU systems they set in the window, so you do not have to cut a hole in the wall to install it.
For a bedroom say 10 x 10 you can use @ 5000 btu it plugs into a standard 120 volt electric outlet. If the room is bigger then go bigger say @ 6000 btu or so. Take your room dementions with you when shopping for a unit. sometimes they have sizing on the side of the unit box.
Wall units are usually larger units. Like whole house 18,000 btu
they slide in and out of the case and use a 240 volt seperate circuit.
Best place to shop for A/C's are Home Depot, Lowes, Sams Club, B.J.'s, and Cosco they buy in large volumeusually give a Good deal I've seen 5000 btu units as low as $89.00
Just don't drop the unit out the window when installing it
From the second floor it will void your warranty. LOL
Good Luck Phil