Dedicated power

Think this through.  Every circuit on a given breaker box leg runs in parallel.  Each device on a given leg is in parallel with every other device.  So....  If there is anything on the same leg in your breaker panel, that noise will enter into the "dedicated circuit" the same way it would if it was coming through the same circuit breaker. 

Most circuits are on 20amp breakers so if your equipment runs OK on the existing circuit, there's no particular need to run a separate circuit.  If your existing circuit is insufficient to handle your equipment load, then a circuit or two might help.  But you won't necessarily eliminate noise from other equipment just because a circuit has its own breaker.  It's all about what is on that particular leg.

If you are REALLY SERIOS about isolating your equipment from circuit noise, IMO, the only REAL way to do it is with a line isolation transformer.  It plugs into a standard 15-5 receptacle (standard wall outlet) and has one or more isolate outlets.  It's what hospitals use to isolate sensitive equipment or high-gain amplifier on that equipment from external noise.  Not the cheapest solution, but IMO the most effective.

As others have stated, there is no reason for a 30 amp line. One dedicated 20 amp line with a good multi outlet power conditioning unit like a Furman SPR-20i should suffice. However, before you even go that far, try using an isolation transformer on your current connection. Don't worry about all the "mod videos" telling you that you need to fool with the ground system. That only comes into play for work benches where you could screw up and electrocute yourself. Any non-audiophile/hospital grade unit from a reputable company like Tripp-Lite will do. You just want to verify that you will hear an improvement. If you go cheap and get noticeable results, spending more money for a pricier unit probably won't make enough of a difference to justify the additional cost.

As mentioned above don't go through the trouble with a 30A line - run 3 20 A lines instead, labor will be the most expensive part anyway it'll only take a fraction of time longer running 3 lines compared to one.

Run all three from the same side of your panel.  Unless you have a very long run 12Gauge Romex will be sufficient.

Good Listening

Peter

I did a 30a line, only one, and it's great. Don't worry about these people needling you for going big and don't use some flimsy transformer. Good wire, good outlets, good power cables, etc. Worth it. 

Mr Carbon is a president of TAMC [Tweak A Minute Club]

Headroom loss for 14ga vs 10ga is less than ¼db @ ≈14A / ≈1600W
See  ieLogical CableSnakeOil AC Wiring

Music power is a fraction of that. Head banger rock @ 120BPM uses about 2 cycles peak energy of the 3600 power cycles in a minute.

Clean screwed connections, not push terminals, make more difference than doubling the wire gauge.