Media center app and remote control for mac mini?
What you need is the right front-end and that is:

Plex

Plex is probably the most Mac-like of all the media centers out there. Certainly it gets a lot of attention on the Mac and runs very well there. Not quite as open or feature rich as XMBC but it plays a quick game of catchup.

It will work with the Apple Remote IR remote control you can buy from the Apple Store. The button mappings are detailed in their wiki.

With Plex installed and running you can access all your media, navigate on a TV-friendly UI using your Apple Remote and use plugins like their Netflix plugin to access streaming content all from one slick interface.

You can download the Plex apps for your iOS and Andriod devices and use it to connect your mobile computers back to your Mac-located content and stream it over the air.