Right, the mixer wouldn't be in the recording signal chain, so the quality of the monitoring chain is just dependant on how much you're willing to spend, and how much flexibility you want.
I'm not totally familiar with the Delta's monitoring software, but if its anything like the Echo Layla's monitoring software, you should simply be able to route any input on the Delta to any output for direct monitoring. In a simple scenario you route each input to its corresponding output (input 1 to output 1, input 2 to output 2, etc). What this means is that the signal going into input 1 on the Delta will be sent out to output 1 in addition to going to your recording software.
From there, you could use a mixer with 8 line-level channels (since its only for monitoring purposes you don't need mic preamps on all of the channels, or any for that matter). Using separate cables or an 8 channel snake (I won't recommend brands here because people take that sort of thing very personally apparently), route the 8 outputs of the Delta to the 8 inputs of the mixer. Set the main fader to unity, set the headphone output to a comfortable level, and use the channel faders to set up a monitoring mix. If you ever need to expand this setup to accomodate multiple musicians its as simple as adding an external headphone amplifier with multiple outputs.
Don't have enough room to accomodate an 8 channel mixer? Don't have the budget for one? Just not that concerned with a totally customizable headphone mix? An alternative, then, would be to route all of the Delta's input channels to a single output channel. This means you would require a mixer with far fewer inputs. In fact, a simple 2 channel mixer would suffice. In this case, I would route outputs 1 and 2 to the mixer. I would designate output 1 to be for "live" sources (ie whatever part I happened to be tracking at the moment) and output 2 to be for "playback" sources (parts that have already been recorded). Route all of the inputs on the Delta to output 1. Additionally, the Delta's monitoring software may allow you to adjust the output volume of each output channel, allowing you to create a customized headphone mix much like before, only doing it in the software rather than on the mixer itself. In your recording software set all of the tracks to playback on output 2 of the Delta. You can then use the mixer to pan them apart or together to your taste. You could have all signals play in both channels, or live sources in one ear and playback sources in the other. That part is all up to personal preference. Again, accomodating multiple musicians would be as simple as adding an external headphone amplifier.
I hope all of this makes sense and is helpful.