Hey Joe,
I totally agree here with Lugia that your case is far too small. A US $ 4k limit isn't too bad, so just use a bit more of that budget for a bigger case, for example the Intellijel 7U * 104 HP is a nice one or even the Pittsburgh EP-420 is good to give you enough "future space". My advice is intially to reduce your budget to 3k, after minus out that bigger case, you should still have left 2k+ for the most important modules to start with. Get started with that (i.e. 3k) and build-up some experience with Eurorack.
Then after a learning & experience phase, you still have 1k left to add some modules that you might then realise you really need after you got some experience. At that point you will thank me on your knees (just joking) that you got yourself a bigger case and kept that 1k in your pocket initially ;-)
Don't believe though that you can stick with that 4k forever, if you really like Eurorack you will have thoughts of selling your house, partner, whatsoever to get it extended with a few more modules ;-) And at that stage again you will be happy you got yourself a bigger case so you still have space left to do so.
Good luck with the planning and kind regards, Garfield Modular.
For review reports of Eurorack modules, please refer to https://garfieldmodular.net/ for PDF formatted downloads