may I suggest that you take a look to any antenna text book including a measurements chapter?. I suggest antennas by Kraus, but there are also specific antenna measurement textbooks, as these:
GE Evans, "Antenna Measurement Techniques", Artech House, Boston, 1990
Microwaves Antenna Measurements. Hollis JS, Lyon TJ and Clayton L. Scientific Atlanta.
1970 (1983)
(Antenna Handbook by Lo also includes one chapter)
You can measure with a linear probe in an anechoic chamber, measuring amplitude and phase, and then composing the results in right hand and left hand polarizations, or you can measure with two CP probes (RH and LH).
Important parameters: difficult to answer, depends on your requirement (gain, beamwidth, axial ratio...). If your main interest is circular polarization, then your design parameter is axial ratio (at the angular range speified), but your design must also meet the requirements you have on gain, beamwidth, sidelobes,....
regards