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.
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.