Going to stick with air cooling for this build.
What about the Corsair 280X?
That's a great case - but it kinda pee's all over your budget and adds sprinkles on top.
The Phantek Evolv is a good case for the money and fits your brief (air cooler).
@tamzzy rightly points out these layouts do have thermal hotspots - but this is the compromise you make when buying ITX within a budget while trying to keep things relatively small and silent.
The vertical solution is a relatively new innovation, and from
@tamzzy's link will probably gain more traction as it ticks all boxes: aesthetics, thermal solution and by extension a quieter units (plus, bonus geek factor). You should re-read reviews of the Phantek evolve - as the thermal scores with decent CPU/case airflow are nothing to be concerned about. Yes, they're warmer when compared to a larger vented case - but that's to be expected. As long as temps are still comfortably within tolerance it's not an issue.
And the below is with a toasty R9 290 - although AIO in use - but a quality air cooler will still do the job: