How old is he? Do you already have a 'non-gaming' PC? Does he have a personal PC that is 'his' that he uses?
That might be some important points to consider. If you don't, that may add a lot of value to getting a PC. If it's just to play the one game, Minecraft, I probably would not recommend it myself - but if you would use it for its other features (research/writing papers/calculations/programming/internet) then it definitely becomes worth it. Or, possibly, if there are lots of other PC-exclusive games he is interested in?
For a gaming PC that you don't build yourself, two companies that are worth a look are CyberPowerPC and iBuyPower. You can order direct from their websites, and usually can find a pretty good overall system for around 700.
Such a system would be able to play most of the PS4 and XBox One games today (that are released on PC, anyway), but would probably find itself needing a new graphics card in 3 years or so (as newer, more demanding games come out - and hoping that it has the power supply to support a new card)... whereas the XBox One will likely last longer b/c developers will target those specifications specifically. You should, therefore, get much more lifetime out of a new console (especially since they just released), but game purchases will cost a little more initially as well.
I don't recommend using a television as a monitor, though... televisions usually have much worse response times and lower resolutions than monitors can support, plus they may be too big to sit near (unless you have one that is <= 27"). I've seen a TV hooked up to a computer and it looked pretty blurry and difficult to read the text (but that was a few years ago). A good monitor is relatively cheap, you can find some decent 23" monitors for around 200 nowadays.
I hope this helps!