Amplifier Measurement

A good plact to start would be gain, Noise Figure, distortion (IM2, IM3)

Input and output return loss also are important.

It depends.
The most common RF parameters are s par, Noise Figure and Po1 (and or IP3, IP2 etc).
Often for a connectorized device, spar phase make no sense, so |spar|[dB] are usually given.
Other "hiden" parameters are important to sell a good quality product, like microfonicity, sensitivity to supply, weight, dimensions, temperature and umidity range, DC dissipation etc etc.