- Get a used Doepfer beauty case (https://www.thomann.de/de/doepfer_a100mc_raw.htm).
They go used for ~50 EUR and include power for a handful of modules.
Or
- Construct a case from spare wood (see http://www.doepfer.de/a100_man/a100m_e.htm for dimensions) or cardboard (). Rails are usually required for that but you can get away with using wooden bars and wood screws to attach the modules with. Get a (used) uZeus PSU and module. You won't grow out of that as fast as with the Doepfer. Heck I even saw a rack made of wooden book shelfs with the modules screwed to them and bricks and tiles as spacers! I guess you can't go any cheaper than that.
To connect the module to your other stuff your mixer should have a -15/-20 db pad switch at its inputs. That should bring your module level to line level used elsewhere. To get outside signals up to modular level, your cheapest option would the headphone amp in your mixer I guess.