I think that my favorite 6x9 folder is an old No. 1 Pocket Kodak Series II. This camera uses 120 roll film so is still easily usable today. Even after all these years the Kodak Ball Bearing shutter on this camera is very consistent and reliable though its' 3 speeds have all slowed a bit. The old, uncoated 108mm f7.7 Anastigmat lens (which I believe is a triplet) that can be set wide open at f/7.7 or closed down at f32. The aperture provides a continuously adjustable range between those two points. Though a bit old the lens is clear and produces some delightful images. It is focused by turning the front lens element. The camera folds up into a light and easy to carry package and it is very simple to use. The old leather bellows is still light tight. It has two 1/4x20 tripod sockets that allow the camera to be set up in landscape or portrait orientation.
On the other hand it does not have a meter or a rangefinder, coupled or otherwise. The small, magnified viewfinder located next to the lens rotates between portrait or landscape orientation. It is small but usable as long as you don't need to be real exact with your composition. While the camera can be handheld it takes great attention to detail on the user's part to press the shutter lever properly without moving the camera. It is far easier to use a shutter release cable and a tripod. Fortunately the camera is light enough that a heavy tripod is not necessary to keep it still. I even use the shutter release cable when hand holding the camera.
Being as old as it is there were some minor problems I have had to sort out but they were pretty easy to handle. The first was that the old door on the camera back that was opened to write on the original autographic film was no longer sealing tight. So, a strip of gaffers tape took care of that light leak. Next, after using it a few times the old red window in the back that allow you to see the film numbers on the backing paper cracked and fell out. It was so brittle that repair was impossible. So, as a temporary fix, I taped a red, transparent piece of a file index tab over the hole. After two years that little piece of plastic is still in place and working just fine.
This camera cost me a total of $25 including a case and shipping so it certainly meets the budget criteria. They are still easily available on-line at very reasonable prices. Just be sure you are buying the No 1 Pocket Kodak which uses 120 film, not the No 1A Pocket Kodak which used 116 film which is no longer made.
If the camera has an old Kodak Ball Bearing shutter I would be relatively confident that it still works though you should probably check the actual speeds when it arrives. I have been told that they are relatively easy to work on but I have never tried to do anything with mine as it really wasn't necessary.