1.Impedance: almost all RF connectors and cables are normalized to 50 impedance. The only exception is that the 75 ohm system is usually used for cable TV installation. It is also an important RF coaxial cable connector with characteristic impedance matching the cable. If this is not the case, a discontinuity will be introduced and lost.
VSWR (Voltage Standing Wave Ratio): Ideally it should be united, well designed and implemented to keep the VSWR below 1.2 in the range of interest.
Frequency Range: Most RF operations are now in the range of 1 to 10 GHz, so connectors must be low loss in this area. For cases above 10 GHz - with a lot of work now done in the 10 to 40 GHz range - there are newer connectors to choose from. They are expensive, because it's the cable itself.