My ten pennies worth......
The Mac Mini will be absolutely fine; I have one and it betters my Meridian CD player (that used to sound very good through my B&W Nautilus 802's). Maybe consider Pure Music or Amarra on the Mini as well, but don't worry about a CD player; a lot of people like myself are ditching them now. The purists will say Spotify is compressed. True, but at 320kbps (assuming Premium service) it can sound very good indeed.
Pay particular attention to the siting of the speakers; how far out from the wall, what you put them on (on top of the desk) etc etc. That doesn't mean spending a lot of money. Experiment with old paving slabs, granite chopping blocks and the like (and enjoy the look on your mum's face when you do!). Maybe consider some of the supports used by pro-studios (as mentioned in the post about the Adams speakers). I think this will be the single biggest factor affecting your sound, particularly as bass is likely to be important for you given the music you listen to.
Finally, if I were you, I'd seriously consider spending a lot less than £900. There are numerous decent amps at £200, pair them with a good £300 pair of speakers, and off you go. Put the rest on one side for when the upgrade bug hits; you'll then be more experienced in what sound you like.
Second hand is probably risky for you at this stage, but don't forget ex-dem kit available from good dealers (I agree you should find a good one so you can listen to equipment. It will save you money, even in the short term).
Hope this helps; welcome to the mad house!