Hiya Tim, As others here have mentioned, MP4 spans a broad range of quality levels depending on the bit depth (8 bit vs 10 bit), chroma subsampling (4:2:2 vs 4:2:0), and data rate.
8 bit 4:2:0 is pretty common as a final delivery format, so in theory if you shot everything framed, exposed, and white balanced perfectly in-camera, and you didn’t want to have creative flexibility in terms of color correction/grading or moving/scaling the video in your edit, you could actually shoot that way. But that’s theory 🙂
In reality, I’d suggest you’re really going to want to record using a 10 bit 4:2:2 codec (or better), as any footage (regardless of codec) will quickly start degrading once you start color grading/correcting, moving/resizing, etc.
As far as data rate, what you’ll want/need will depend on how much detail there is in your scene and how much movement there is. As a reference point, Sony’s FX30 (the lowest $1800 entry point to their cinema line) will do 1080p240, 10 bit 4:2:2 at 50 mbps (using an IPB codec) or at 222 mbps (using an all I-frame codec).
And as others here have mentioned, if future-proofing is a big concern, you may want to consider shooting at 4k (or UHD) instead of 1080p (HD). But of course this can bump you up into a higher price bracket not just for the camera, but also for the memory cards, storage space, processing power, etc…
Sounds like a fun/interesting project. Best wishes for it!