The Mac mini makes an excellent home entertainment hub. It's so tiny that it's virtually unnoticeable and, because modern Mac minis are extremely low-power, it can be left running 24/7 without running-up a huge electricity bill. At 12dBA it's also quieter than an old-fashioned library, so won't disturb your viewing pleasure either.
In short, it's the perfect home entertainment tool.
Choosing a model
Even the slowest processor in the current Mac mini line-up will be able to handle every audio and video playback task you throw at it (including 1080p HD playback), and the minimum spec of 4GB of RAM is also more than enough.
Focus instead on storage, and possibly upgrade to a larger 2 or 3GB hard disk. Alternatively, look into getting additional USB/Thunderbolt hard disk storage - which will also be much cheaper than a factory upgrade. After all, movie files are pretty big - typically in the order of multiple gigabytes for a standard 90 minute film at 1080p HD resolution - so even a modest movie library can easily fill a disk.
An external USB hard disk, such as a G-Drive, is an ideal Mac Mini upgrade and will allow you to store more movies
Attach your Mac mini to your TV via HDMI and you'll essentially turn the TV into a large monitor, complete with sound output. The Mini will probe and set its resolution automatically but if there's an error in resolution settings - usually indicated by a blurry image - you can set it manually by opening System Preferences and clicking the Display icon. Then select the Scaled radio button alongside the Resolution heading, and select from the list below. Check the TV's manual to find out its maximum resolution. Pro tip: here in the UK, TVs described as HD or HD Ready tend to be 720p (1280x720), while those described as Full HD are usually 1080p (1920x1080).
Lowering the resolution on the Mac Mini might make on-screen elements larger, but could blur the image slightly
However, ensure the TV doesn't have overscan activated, which will zoom into the desktop slightly - also causing blurriness - and crop-off the edges of the image, possibly hiding the menu bar. How overscan is disabled differs from model to model of TV, and you should consult the manual (or consult Google), but selecting a "PC" or "Gaming" profile for the HDMI input might do the trick.
Making the screen bigger
If the desktop is simply too small to be seen from a distance, such as your armchair, there are two possible fixes.
The first is to switch to a slightly lower resolution in System Preferences, as described earlier (pro tip: hold down Alt/Option when clicking the Scaled button to see a wider range of resolution options). This will result in a slightly blurry image but it's possible to live with this.
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