Right now, I think you're connecting to your integrated via a 3.5 mm plug to RCA connectors (red/white). If this is the case, and since your amp is analog which leaves you with no choice, you're using the DAC in the apple TV.
However, if you have a home theatre receiver or plan on getting a DAC (the come in all price ranges) then you're going to want to bypass the DAC in your computer/apple TV/whatever by using a digital cable out. I think Apple products only have optical/toslink. A lot of people seem to think coaxial is far superior to optical and some think otherwise etc. because of jitter etc (the jury is out on that topic too.
Either way, if you have an Apple there is only one choice. However, there was this good article from six moons, where the reviewer did a shootout with relatively inexpensive ($150) toslink cables and found them to be equal to very expensive coaxial cables... so this is good for Apple people.
Only two cables met his expectations. The "Wireworld SuperNova+ MKII" and the "Van Den Hel Optocoupler". They're both glass toslink cables. I'm still waiting for mine so I can't say if it is an improvement.
http://www.6moons.com/audioreviews/toslink/toslink.html
Oops, re-read your post. If you have surround, then you have a digital processor. In that case, I would use a toslink to send out the ones and zeros and use your surround processor to do the DAC conversion.
By the way, find out if the output on the Apple TV is a "mini-toslink" or regular toslink (which is synonymous with optical). You can buy an adapter, but Van Den Hul makes a mini-toslink to toslink cable. That's what I chose.
I basically use my Macbook and send all audio... divx movies, youtube, itunes (Airport Express/files in AIFF/MP3), whatever, through a toslink cable into my cheap DAC ($150 entech 205.2) which I connect to my cheap analog integrated. Sounds good to me.
I have to admit there wasn't a huge diffence with the cheap DAC and the DAC in my airport express. There was less grain, and the images were bigger and I guess the sound was larger, but I have a pretty basic amp. Your system should be much more capable of discerning sonic differences.
By the way, different file types make a difference. If you can ripping CDs in bit for bit formats like AIFF (or WAV, but this is not ideal for itunes because you can't tag tracks as well) is far superior to MP3 or lossless. In fact, I found (granted it's on my non-hi resolving system) lossless sounded really compressed and I think I preferred a high bit rate MP3 (320kbps) over it. AIFF is definitely better. You'll have to see for yourself.
You should go to the "wavelength" site (their Brick DAC..tube) and have a read, it explains things much better than I would. If I could drop that kind of cash, that would be my new toy. A lot of reviews like the Benchmark DAC 1 (SS), but then I wonder why there are so many for re-sale. Either way, both these items go quick.
I'm pretty new to this and didn't want to spend a mint while I figured stuff out. Hope this helps.