Do not connect your Mac Mini to Denon AVR. That is wrong for variety of reasons. Instead, connect Mini directly to your TV using the input on your TV that is designated for PC connection. Then connect Mini to Denon using toslink optical cable. A universal remote (such as Harmony) will allow you to switch inputs effortlessly.
Your Mini is a computer. It outputs a video signal using RGB 0 -255. Most consumer electronic devices such as BD players and cable TV set-top boxes output 16 - 235. Your TV expect the 16 - 235 input on all inputs except those dedicated to PC connection. If you connect your Mini to the Denon together with multiple other devices, and then feed one HDMI cable to your HDTV, you will most likely experience subpar picture quality from the Mini. Specifically, your blacks will be crushed (loss of detail in dark areas), and your highlights will be blown.
The other problem with this connection is overscan. Your HDTV will normally apply some overscan to get rid of assorted junk that sometimes appears along the very edges of video signals in TV broadcasting. Consequently, the picture you are seeing from set-top box is likely scaled. You don't want that with your Mini. Instead, with your Mini you want to get perfect 1:1 pixel mapping (no scaling) especially if you care about sharp text and icons.
So, flip through your TV manual, find the input that can accept PC signals, and connect your Mini to that input. You don't have to to anything extra to get perfect sound via optical output (using mini-to-Toslink adapter).
