I have a system very similar to what you presently have and have been using it for over 4 years without any issues. i have never had a dropout or failure to play music. All you need to do to get started is a DAC, amplifier, and speakers. You may want to upgrade your Apple Airport Router. Refurbished Airport Extremes are routinely available for $129.
I have an iMac and a MacBook Air with our music files all on iTunes on both computers. I have 3 Apple TVs and an Airport Express all connected to stereo systems in different rooms. The Apple TVs and Airport Express are connected via an optical cable to DACs which are connected to an amplifier. I can stream my music from either computer to either stereo system wirelessly. My wife and I use our iPhones or iPads as a remote control with the iTunes Remote App. So we can be in any room and select any music file or playlist and stream it to that room. As long as the amplifier and DAC are turned on anyone can operate the iPhone or iPad as a remote and play music in any of 4 different rooms. In fact my 2 1/2 year old grandson can operate my systems on his iPad. He has his own playlist and routinely plays music in our rec room.
I have an iMac and a MacBook Air with our music files all on iTunes on both computers. I have 3 Apple TVs and an Airport Express all connected to stereo systems in different rooms. The Apple TVs and Airport Express are connected via an optical cable to DACs which are connected to an amplifier. I can stream my music from either computer to either stereo system wirelessly. My wife and I use our iPhones or iPads as a remote control with the iTunes Remote App. So we can be in any room and select any music file or playlist and stream it to that room. As long as the amplifier and DAC are turned on anyone can operate the iPhone or iPad as a remote and play music in any of 4 different rooms. In fact my 2 1/2 year old grandson can operate my systems on his iPad. He has his own playlist and routinely plays music in our rec room.