The problem I had with the passive set-up was that the desk outputs too hot a signal for the computer interface, which results in a lot of clipping. The passive attenuator worked, but resulted in a noticeable drop in signal volume at the desk, and some loss of high frequencies.
So it sounds like you loaded down the output too much, but to comment we would need to know specific details, mind you to understand what are trying to achieve would need specific details anyway, so more information would be useful.
The computer interface also introduced noise, although that was solved by simply grounding the chassis to the desk chassis.
So you already have a computer power supply with a noise problem (sounds like a double insulated supply) which does illustrate why using a random power supply could cause problems, or on the other hand might not cause problems.
There is more to the project than just wanting to get a desk output. Once this works, I plan to add some kind of VU display for each channel, and maybe even its own microphone inputs. At this stage, I'm just wanting to keep things simple though. Get a good starting point and then build upon it.
Fair enough, sounds a good idea to start with in which case you probably want to start taking this into account as you begin the build so you don't just end up making something several times over.
Some of the cheap power supplies may be noisy, but some of them are expensive supplies, and I would be adding some caps on input anyway just to add smoothing. I have a box of various reclaimed electrolytic to use.
Its not always cost, but more design requirements, for example a power supply designed for a printer might allow for higher surge currents, while noise may be less of a consideration.
On the other hand one of your supplies might already provide a dual rails, or you might have a 24V supply that is grounded which could cause issues even with decoupling and a virtual split rail, again without more information we wouldn't know?
the circuitry is fairly simple, just set-up your op-amps as Voltage followers (i.e. with the inverting input connected to the output, and use the non-inverting input) - Technically in this set-up there is no 0V rail involved so you don't even need to worry about the virtual ground.
at unity gain most Op-amps will provide pretty good results