Yeah I concur with what Mike has said with the budget you have you can have pretty much anything
If you want to build your own SFF rather than using a Shuttle then Silverstone do some lovely cases their Sugo series are a real pleasure
or the TJ-08 their uATX mini tower.
The Sugo 1 and 2 (SG-01 and SG-02) are both uATX cubes which take full size components. Both look fantastic with the SG-01 having an aluminium front while the SG-02 having a plastic front which still looks top quality.
The Sugo 3 (SG-03) is pretty much as small as you can go but with overclocking being in the works you would have to carefully select the CPU cooler as the isn't a whole lot of room available! If your interested in this case say and I will talk through a few more of its quirks and what I think it needs in the way of cooling to make it work efficiently, mainly a vent at the back top or an extraction fan there to remove hot air.
The TJ-08 is nice to work in bigger than the SG-03 and more conventional in its layout. Airflow is all right but the fans can be a bit loud so I would suggest replacements.
A duel slot graphics card cooler which exhausts out of the case can be a boon in SFF builds as they remove a lot of the heat from the system where other cooling solutions dump that heat into the case, which then needs to be removed this can be harder as airflow on the whole is more restricted.