Even though Shure SE846 are good headphones they are tiny IEMs,and I personally think spending £1400 on a headphone amp+DAC combo to run them is a waste IMHO OFC- maybe if you had a decent pair of full sized high impedence headphones perhaps with much larger drivers which,but half the reason for IEMs is so they can run easily off portable equipment like iPods,etc and this is why they are also noise isolating.
If you look at the impedence of the SE846 is only 9 Ohms,so they are quite low impedence headphones so really don't need expensive amplification. This is much lower than my full sized Grados which are only 32 Ohms.
Also regarding spending £1400 on the Chord Hugo - you are basically paying for a nice box and a brand name.
Yes,the marketing is all about its custom bits but honestly we have had a few decades of DACs,etc already -it is not like 20 years ago when these electronics were very exclusive and low volume and it was all new and experimental,these things are very well characterised now - read what nwavguy said on his blog,ie,the chap who designed the ODAC. I would even argue a decent sound-card probably would be fine too,but I find DACs are more flexible(and more importantly somewhat isolated from a computer).
Many companies try to up-sell their stuff by boasting about XYZ random stuff(which might actually not be needed in the first place) and the hifi press will be quite happy to wax lyrical about it all. I mean I have listened to all kinds of format,records,reel to reel,mini-disc,HDCDs,SACDs,etc,and one of the most important aspects I came to realise was the mastering as much as the quality of the playback format.
If you are buying the Chord Hugo,do it because it looks a nice bit of kit(which it is),but I would be very dubious about whether it will magically make anything sound 10x better than going for one which is one fifth of the price or less.
So I would be tempted for you to listen to some DACs in a shop from cheap to expensive,ignore the salesman,ignore the price and see if you actually hear a difference.
I actually listened to a £100000+ DAC,headphone amp,CD player with a pair of £5000+ headphones and you know what,me and my mate actually listened to another set of headphones from a small relatively unknown company running through a battery amp which probably cost closer to £2000 though a portable music player using FLAC(and our phones also) and it actually sounded better.
If I were you I would actually spend more of the budget on the amplification and/or speakers themselves. I have seen the Chord stuff at shows and it is very nice,but I was always felt you are kind of paying more for the design in some ways.
That's a shame!