Hi, Balder
There is some good, but disparate, advice on the forum - you'll have to decide which suits your situation best.
As a long-time user of Apple gear, I thought I'd throw in my two pennies. Given what you have said so far, my suggested approach for you would be to play your music straight from your Mac, preferably via Asynchronous USB if your Saturn R can accept it. This will require your Mac to be close to your DAC, but you can then control iTunes on your Mac using the excellent (& free!) Remote app on your iPhone. This would be my preferred approach as it should give you the best sound quality for near-zero outlay.
If your Mac is too far from your DAC for a USB cable (no more than 5m, but the shorter the better), you could use either an Airport Express (AEX) or Apple TV as a wireless (or preferably wired- it's more stable) 'digital data source' to get the data to your DAC. A couple of points to consider, though: the AEX suffers from jitter, especially the 2nd gen device. I have three AEX boxes, two 1st gen and one 2nd gen. I can't use the 2nd gen AEX with my Audiolab 8200CDQ (CD & DAC) - the DAC loses 'lock' about every few seconds making it impossible to listen to. However, the same AEX works with my Beresford Bushmaster. So, whilst these devices should 'just work' (like most Apple kit), using them with 'high-end' kit can throw up some issues. I don't have an ATV, so can't comment on that.
Final point. AEX and ATV can only send data to a DAC via optical Toslink cable, and are limited to 16 bit 44kHz data rates. This means you can't use asynchronous USB, where the DAC 'pulls' the data using it's internal clock which should result in better sound quality. Being limited to 16/44, AEX and ATV cannot transfer Hi-Def files, and are therefore not very 'future proof'. You may not be bothered about these two points - I am willing to sacrifice sound quality during 'social listening'! - but I thought I'd mention them before you spend £100 on an ATV or AEX.
I hope that's been helpful - it was intended to be!
Good luck!