Dedicated 20 amp circuit. 10/2 or 10/3?

For most folks, a 12/2+G or 10/2+G run from the 'quiet' side of the panel is perfectly adequate. If you have big power hungry monoblocks, then a 10/3+G providing 2 circuits is still more than adequate. 

In an existing house you may not have panel space or the luxury of picking a 'quiet' side of the panel and electricians rarely leave service loops adequate to rework loads by re-homing breakers. In that case an solation transformer although hugely expensive may be worth it to you. For most, good power conditioner will have to do. 

In any event, a digital oscilloscope, preferably with spectrum analyzer capabilities is really the only way to see how clean or dirty your power actually is. 

10/2 and run more than one dedicated line while you are at it.

I have a pair of class A mono blocks, I ran one 12/2 conductor twenty amp circuit to a Cardas 4181 receptacle. From the wall the power cord goes to the power conditioner, then all my gear plugs into the PC. Running full load with some volume, I am pulling 9 amps of current . Not sure what your gear is? #12  is adequate for most systems. But run cable for where you will end up.

Keeping all the audio on one leg helps reduce ground loops. Your system is probably not going to draw enough current to need both legs.

Circuit breakers at the Bus? If you are running a dedicated breaker for each piece of equipment (you are going to need some 2 and 5 amp breakers, and with no AC motor loads I would ask why have a separate circuit for everything?... I would first consider a sub panel to save on all those copper runs (and to prevent leeches, or "other" circuits invading), then yes alternate between the bus (legs), or left side right side in the panel, and try to keep the loads balanced, and the circuit breakers and wires correctly sized for the designed load ("over sized" circuit breakers and wire is not a CURE for anything). Any 220V breaker will already be feeding from both bus bars. Chances are good that your main panel is presenting an unbalanced load now. If a sub panel is separate (downstream) from the main service, through a  fused disconnect and a sub panel main breaker, I would consider Isolated Ground Outlets, and possibly (if the current NEC allows) a separate grounding systems for that sub panel, or at least those outlets.  A more extreme$$$$$ (but effective) measure would be a complete new service, much like Fremmer did at his house (see his videos). But please consult a Master Electrician, I have not professionally practiced since 1994, and am not familiar with current (lol) code.. The National Fire Protection Assoc. publishes the updated National Electrical Code, and licenses professionals in an attempt to keep us folks from burning, or exploding, things and those we love and cherish.