Hi Swippy,
I have just upgraded from the Bose active speakers to a Fatman itube amp and ipod dock which I am very impressed with. I bought it from bestpricehotdeals.com for £125 delivered. I bought the Tannoy F1 custom speakers to go with it and they sound superb I paid £85 delivered from forumhifivisual.co.uk.
I already had a dac (Fubar11) which I paid about £100 for from Russ Andrews again via net, I think its a bit more now .
I hav all my music in lossless on the pc which is in a room approx the same size as yours.
The music played off the ipod direct into the amp is very good without the dac and it would come under your budget with the Tannoys.
Hope this helps, there are reviews of the fatman and tannoys on the what hifi site.