I've had maybe 4 cameras over the years mounted on my wall/ceiling.
If you mount on a wall (near ceiling height), you should be fine with any camcorder. 1080 or the newer 4k ones. This is the view most live streamers use. You can get one new for probably 150 range now.
If you mount to the ceiling with 8-9' ceilings, you will have problems with the lens. You will need a wide angle lens. For this, you can get a DSLR camera, and a wide angle lens used for indoor real-estate listing photography. This is my current setup and I like it a lot. I got a used DSLR for 150, and the lens was 200.
You will need a power cord adapter for either type, so you can leave it on for hours at a time and not have it drain the battery.
To get the video out, you have two options: First is to climb a ladder or on your table and pull the SD card out and load it into your computer. Second is to do what live streamers do, which is use the HDMI out from the camera, and plug that into your computer via an HDMI capture box/card. This adds another layer of complexity. But, you can leave the camera turned on 24/7 and start and stop recording from your computer, and save the footage directly to the computer's hard drive.
I'd personally recommend climbing the ladder if your are starting out. The live capture stuff has a large learning curve.