I remember a couple of years or so ago it seemed like there was always a different thread/discussion going on related to dedicated circuits. Either here in the preamps/amps forum or in misc. Anyway, you might find some of those discussions interesting and informative, so if you use the 'search discussions' function up on the top of the page and try a search engine such as "dedicated circuits" (or something to that effect) I bet a lot of interesting results would come up.
Anyway, I have my amp, preamp, and digital source all on one dedicated 20A circuit, and I have tow dedicated circuits that I am not using right now. So I really think that one 20A circuit would do it for you,
BUT,
as far as labor goes, the actual work of putting three circuits in (which is what I did) is not a whole lot more than putting one circuit in. The Romex is an added expense, but still, it I was going to put one in, I'd put at least another one in, and that would give you some flexibility to experiment with.
As far as the hum and "interference" (RFI?), that might be cleaned up simply by having a dedicated circuit. As I typed in my first paragraph, there is are a lot of great threads on the subject.