Considering gettting a 2010 mac mini as a media center pc. is this a good idea?
As everyone here has mentioned, the 2012 is currently the best choice for a used Mini, at least in terms of functionality.
But, as I am typing this post right now on a 2010 Mini, let me go ahead and put a plug in for it. If all you are doing is
playing media, a 2012 Mini is going to be overqualified in terms of CPU power. In fact, the 2010 Mini is going to be overqualified.
On the plus side, the 2010 has a Core2Duo processor (which, while antique at this point, is still usable), the ability to upgrade its RAM to 16 GB (which, again, you really don't need for serving media), and the very nice Nvidia GeForce 320M GPU. It has HDMI and Mini DisplayPort ports; the HDMI can drive up to a 1920x1080 display, and the mDP a 2560 x 1600 display.
On the minus side, it is now a fairly old machine. So hardware issues could become a problem. The ports are fairly old (no USB3, no ThunderBolt), although it does have a Firewire 800 available, so you can get at least a little speed out of external drives. Also, while Apple still supports the 2010 with the latest version of macOS, there's no guarantee that they will continue to do so in the future. And yeah, if you have a TV with a higher resolution than the 320M GPU can manage, you won't be able to drive it directly from the Mini.
In any case, if you can find a good deal on a 2010 machine, I would go for it. It is still quite a capable performer for many tasks, especially for things like serving media.