There are many options available for the fan of rangefinders with a small budget. But, you will be mainly limited to non-interchangeable cameras and most of the options will be fixed.
The Canonet QL17 camera comes with a lovely 40mm 1.7 lens. This is a lovely little camera and very easy to use. You can buy this for under $100 nowadays.
Several different cameras with similar specification out there at this time and all of them are perfect options for a cheap camera.
The Konica C35 has a 38mm 2.8 Hexanon lens, The Olympus 35RC has a 40mm 2.8 Zuiko lens, the Yashica Electro comes with the outstanding 45mm 1.7 Yashinon lens is possibly the smallest rangefinders out there. The Minolta Hi-Matic E with 40mm 1.7 Rokkor lens which could be the alternative with a rangefinder.