You can do the Airplay. I use an external dac and a traditional stereo amplifier so I have to have the TV on. But - there are plenty of threads on here with people discussing how you can have the TV off using an AV amp.
Or you can use an Airport Express for airplay only and not use it for access to the internet. You can connect it to your amp either digitally or by analogue. This is what I do. I use Apple TV if I want the TV on, Airport Express otherwise - just change the input on the stereo amp.
The old model Apple TV is limited to the apps that Apple put on it. The new model has access to the App store. If you mean the Airplay app (difference between the two Apple TV's) you don't actually use an app on the Apple TV for airplay. No matter what is showing on the Apple TV screen, you just toggle the Airplay symbol on your phone or your computer to the Apple TV, and the music starts playing through the Apple TV. You can make adjustments on your phone or computer. You can also use the Apple TV controller to rewind, pause etc but in practice the controller is much more reliable on the new Apple TV.
The Airport Express works in a similar way. You configure the express and give it a name like Mordo's speakers, but then you never touch it. You just toggle Airplay on your phone or computer to the speakers. You control it fully from the phone or computer.
I have both the old and new Apple TV's. I would advise you to buy the new one. Its a big step ahead, the old one is limited and feels a bit clunky buts its OK. The new one doesn't have digital audio out, as you noticed, but you can digitally pass it through your TV either by HDMI to your AV amp, or like me, by Optical from the TV to your DAC and then by analogue interconnects to your traditional amp. This works flawlessly. I did this even with the old model Apple TV3 (never used its digital sound output).
The 32GB new Apple TV, rather than the 64GB seems to be fine for the minute. There is a lot of discussion on here over how much storage people are actually using, and most people are hardly using any. This may change if some popular apps actually start taking advantage of the storage, but as it stands I can't use the storage even if I wanted to.
You could get the old model plus an airport express for just a bit more than a 32Gb new model Apple TV, and use them both for audio airplay, but I would go with the new model Apple TV.
The main thing you need to have a nice experience using your mac through the apple Tv is a great network. Ideally ethernet from both the Apple TV and Mac to your router, but at least excellent wireless signal and a good router. Airplay iTunes homesharing without a solid network is extremely frustrating.
Also, if you are using stereo equipment rather than an AV amp, it might have a DAC built in and digital inputs since you have spent a lot of money. Some of the newer stereo amps do now.