Hi Ethan. This is going to be near impossible at your current budget. You can easily blow through $400 on a case and cables. Any modules that you can squeeze into that budget will be severely limited in their usefulness, as you likely won't be able to fit in all of the most basic components of a functioning synthesizer. I would highly recommend saving up AT LEAST a thousand dollars/euros/etc. to get close to something that is a bit more than a single oscillator and filter with onboard VCA. Save up for what you really want and buy those modules one at a time if necessary, and don't just buy something because it's an affordable alternative.
The Behringer Crave is a good inexpensive semi-modular alternative for under $400. It has everything you need to get started making some sound and you can incorporate it later on when you start building a rack.
What equipment do you currently have to use with a eurorack setup?