How should I organise four weeks of case interview preparation?

The most important thing here is narrowing down the noise. There is a lot of content flying around, and you need to work hard to focus on what's important (much like when solving a case). Be careful with the “number of hours” and “number of cases” mindset - this isn't the right approach! That said, if you have 4 weeks you'll probably need 20+ hours per week and want to aim for 15-20 cases. This isn't to say you're gaurenteed to be ready by then, but it's a good thing to aim for.

I recommend the following:

1. An initial planning session with a coach: 1 hour with a coach now will have a productivity multiplier effect on all your efforts moving forward. They will figure out what materials are best for you, guide you towards the best ways to learn, and come up with a preparation plan with you.

2. Leverage free resources first: Poets and Quants, SpencerTom, Google, etc.). Leverage these options, read-up, and over time you'll get a feel for what you really need and where you really need to invest your hard-earned $

3. Case with other candidates: Casing with other candidates is free. Not only do you get to practice casing, but you get direct feedback. Additionally, you learn a lot just from casing others. Finally, from other candidates you'll learn which materials/coaches are helpful.

In summary, while free options don't beat paid options, you can use them for a while to get a feel for what works for you. Have an initial coaching session to get you on the right track, then go the paid route when it's clear either 1) You are stuck or 2) It's clear the paid route will improve your productivity/progress