You can look up the specs for your AC unit and see what you need. Mine is 14.9 amps max and will start up connected to a 15 amp circuit. It trips the breaker when any other load is added, so I never use it.
The best solution is to install a 30 amp circuit to use, which should be enough to run the AC and leave you about 15 amps for other things, including the refrigerator which should use anywhere near 15 amps by itself (check manufacturer specs for requirements).
For me, on a 15 amp circuit, my refrigerator runs, my electric water heater works, and I can use the microwave at the same time and still have enough power for the computer, television, wi-fi network, lights, and misc. other things.