I think any relatively short (under 9") graphics card in that price range would work, sufficient power supply permitting. The length limit I took from someone on the HP support forum and you should verify yourself, but it's a micro ATX system so it's very unlikely a really large card will fit.
MSI offer a short GTX 760 which might be worth considering for the top end of budget - http://pcpartpicker.com/part/msi-video-card-n7602gd5ocitx also Zotac "Amp" version - http://pcpartpicker.com/part/zotac-video-card-zt7040210p
Most all GTX750 Ti's will fit and they are considerably cheaper, but still quite good (no PSU upgrade needed either) - http://pcpartpicker.com/part/evga-video-card-02gp43751kr
A few Radeon R9-270's are short enough, but most R9-270X's I could find are too long. They are just clocked a bit lower than the R9-270X - http://pcpartpicker.com/part/powercolor-video-card-axr92702gbd5tdheoc
Finally Radeon R7-265's also usually come in at just under 9" so might be OK and offer great performance per $ - http://pcpartpicker.com/part/xfx-video-card-r7265acnj4
Rank in terms of performance (fastest to slowest) GTX 760, R9-270, R9-265, GTX 750 Ti. Most of the GPU's I mention are in these charts for quick performance comparison purposes.
If your system came pre-installed with Windows 8 and has UEFI then you may need to disable Secure Boot to change the video card as per these instructions.
Edited by jonuk76, 07 December 2014 - 09:43 AM.