Hi Mike! 2 x 20A would be my preference. You want to do 20A runs for audio because you get thicker wire inside the walls, that lowers wire resistance for lower impedance to the amps, allowing better damping on amps with undersized transformers. You can use 20A hospital grade outlets. But most electricians will only stock the single plug outlets for a 20A circuit, but you can replace it with a 20A Hubbell duplex on your own.
There's no such thing as 10A circuit, minimum now is 15A as a standard circuit. This would probably be enough for anything you would throw at it, but you don't get the 12ga thicker romex in the walls, you only get the 14ga standard wire. Since the labor is most of your cost, installing the thicker wire is worth it.
You can gang a couple duplexes together in a longer box if you want more outlets on each circuit, but mark which outlet comes first, you'll want to put your power amps on that one.
The AC will put some noise on the audio circuits.
Ask the electrician to put both of your audio circuits on the same leg, the opposite leg of the AC circuit. 240V service is made from 2 legs of 120V running in opposing phases to create the 240 when added together. Audio system only needs 120V, so only one phase is needed. It will still work if some audio components are on one phase while other audio components are on the other phase, but [the internet] says that the sound is better when all audio components are on the same phase. The phase, or leg is determined by where the breakers are physically installed in the panel. The phase alternates with the vertical spaces in a column of the panel, and left/right side spaces are opposite phase.
Like this:
X O
O X
X O
O X
So you would put all of your audio circuit breakers on either all Os or all Xs. Put the AC circuit on the other phase.