I'm thinking of re-installing Windows Home Server to an SSD as system drive. They cost quite a lot, but I'd like the safety of a flash drive. What is the minimum system drive size, would 32GB work fine?
No. The documented minimum size is 80 GB. In reality it will let you install on a drive around 65 GB or so, but definitely not 32 GB.
As I understand, Home Server does not "land" files copied to the shares onto the system drive anymore, so it should only be a matter of a comfortable size for the OS to run, correct?
That doesn't matter. The OS will check and if you don't have a drive of sufficient size, you can't install WHS.