If you provide a bit more information about your set up it would be helpful in giving a more useful response.
1) what devices will output the files (TV, iPad, iPhone etc.) in your home?
2) are your "archived discs" all DVD or also Blue Ray?
3) What audio set up will you use with your Denon (stereo, surround etc.)?
4) Will you have this Mini also do iTunes or strictly your own file set up etc.?
I'll get the ball rolling here and hopefully it will give you some things to consider -
The Mac Mini is more than capable of outputting media files. The limitations of the Mini has more to do with Apple and its lack of support for HD audio (as in DTS-Master as found on some Blue Rays etc.) If you only have DVDs, it will play back the type of associated audio just fine. A couple of excellent software options for your set up might include Kodi (previously XBMC which is free) or Plex (which is a bit more of a client server set up now and was spun off XBMC). These software options provide an excellent front end experience on TVs. My taste is for Kodi as I find it does exactly what I want.
If you have a system that is surround, you want the best audio, the work around on the Mini is to install either Windows or Linux and then a software like Kodi. These operating systems will pass through the HD audio to your Denon unlike OSX.
Storage - don't be too surprised but even an external drive that is USB2 is enough to move data along without issues. The Mini 2012 has USB 3 and that should be ideal for external storage of whatever size you want. There is the Mini-Stacker series of external enclosures that as the name suggests, can be stacked with a Mini (same footprint for the most part). There are also 3.5" and 2.5" external drive solutions that should work (and don't forget to make a second copy at least in case of drive failure as in get yet another drive to back up your media files). Some people prefer to go to a NAS route where the storage is accessed from the network rather than directly attached to the Mini. It has advantages and disadvantages like anything else but if large storage is in order, the advantages outweigh for most, the negatives.
Handbrake - A well established tool that has its place IF* you require conversion and compression of your files. I find it is particularly useful for files meant for iPhone and iPad type playback and absolutely a sin to use if you want to play back on your TV (and want top quality playback). Various software can play back MKV, M2TS (blue ray native) and VOB (DVD native files) without being converted or compressed. MKV is nothing more than a "wrapper" and thus no compression unless you use a software that provides compression as an option.
Software tools -
MakeMKV is probably the best tool on the OSX side for Blue Ray. There are other tools out there but this one consistently gets a nod as the "go to" tool. There are various other tools for DVD as well. MakeMKV works with Windows and Linux too.
Windows side - ANYDVD HD, MakeMKV, ClownBD (a combination of free software that creates a final file that has the video stream, your choice of audio and even subtitles etc.), DVDFAB etc. Yes, the Windows side sadly is really the workplace for many toolsets to get things done for digital archiving.
Alternatives to Mac Mini -
If a front end is important, then you may consider a proper streamer type of solution such as the NVidia Shield TV along with installing Kodi. It offers excellent playback along with other goodies such as streaming services like Netflix and Hulu as well as Google gaming stuff (sorry, not a gamer so wont comment on that end). It also can play higher end music files if that is your thing. NVidia Shield TV also has the advantage of being 4k capable if that is important.
If a front end is not as important and you simply want a list of your media files, the top dog here is the Oppo 103 and 105 series of Blue Ray players that also provide some streaming services but more to the point, do a premiere job of playback of networked files (but no ISOs) with respect to video and audio output (up to 1080p).
As you can see, there are many things to consider but if all you want is playback of DVD to your TV, then consider the Mini with Kodi or Plex and I advise you get an external drive for media storage that attached directly to your Mini HTPC player or advance to a NAS (network attached storage). Use Handbrake only for creating files for iPhone/iPad not for your TV playback.
Look forward to your filling in the blanks on the above so others too can lend some advice or things to consider.