A blank Tutor-based installation uses 341 MB in the data/ folder – this includes MySQL database (283 MB), MongoDB (17 MB) and the Android app (21 MB). I’d say that the amount of space that you need depends on how many students your platform will have, how frequently they will have to upload files, how big these files will be, how much videos your staff will upload, how large they are, etc. It could end up being anywhere between 100 MB and 100 TB.
For memory, I was told by a system administrator who runs a large Open edX platform that the LMS requires up to 16 GB/500k unique users/week.