Dance Studio setup - Would this work?

I'm looking to setup a media server in a dance studio using the items in the diagram. I currently have all the hardware except the Mac Mini. I'm looking to get one from 2009 as they have a DVD player. The setup I have in mind is as per the diagram.

Constraints are:

Good sound

Ability to play DVD

Ability to switch/ fast fwd/back/pause to any dvd track or music file within seconds

Ability to switch from viewing video on the TV to music within seconds.

Wireless control

I can't put the dance files on the Mac Mini as they are menued and this gets screwed up when copied to HDD. The teacher wants quick-fire access, minimal hardware and to remove all the clutter of current cables and ancient media equipment.

So, I'm looking for constructive advice from those here in a better position than I to decide if my plan is sound or sucks. Many thanks.