Question

If you had to both encrypt and compress data during transmission, which would you do first, and why?

Answer 1

Encryption Before Compression is considered most suited

Because if you compress it first there is chance of a side-channel attack method known as a "compression oracle" can be used to deduce plaintext data .
So if Security is you priority then do Encrypt first but this method has a flaw Compression will not be that much efficient as Compression looks for patterns which are kind of absent in encrypted data.

So this thing depends upon priority
Security Or Efficiency

Hope this helps.