I don't think you'll get the combination you are looking for: size, manual control, focal length. If the camera is under $100, it will probably have no manual control at all, and probably have a wider lens [e.g. the XA]. If it is under $100, and has the level of manual control you want, e.g. some of the 70s rangefinders, or similar, it'll not fit the pocket. Almost all of the higher end point and shoots that have all of these features will fit in a jacket pocket, but not a trouser pocket, and they'll cost a lot more.
I've been through a similar quest myself, so I'm not being dismissive. It tends to be: small, manual control, cheap. Pick two of three. If you add in the focal length requirement, pick two of four.