Which 2014 Mini are you considering? 2014 was not a very good year for the mini, the top of the line 2012 Mini is 50% faster than the top 2014 Mini, for example. And they went to soldered, non-upgradeable RAM in 2014. You definitely want to avoid the base 1.4ghz/4gb Mini, it is incredibly slow at everything. When shopping, get a Mini with at least 8gb of memory, and the 2.6, 2.8 and 3.0ghz models also have a better graphics chip than the 1.4 version (although that might not make much difference for your use).
The 2012 Mini has an IR receiver that works with remote controls, so some people like that for home theater. The quad core i7 is probably the only 2012 still worth considering, but the HD-4000 graphics are showing their age and Apple will soon drop support (they have already dropped the 2011 mini).
If you can afford it, the base i3 2018 Mini is a much, much better machine all-around than any of the 2014 models. You can find them in the Apple Refurb store for about $600 with the same warranty as new.
Let me know if you'd like this thread moved to the Mini forum.
