First of all, the card you have picked will be fine at 1440x900 for diablo 3. Diablo 3 should be less demanding than Metro 2033 at medium detail (with Dx11 enabled) and therefore since the 6670 can run Metro 2033 at 1680x1050 (higher than 1440x900) at ~35fps average then it will probably run Diablo 3 at around 45fps average (source http://www.tomshardware.com/reviews/radeon-hd-6570-rade...).
Second, the PSU you have picked is worse than nothing (stay away from Diablotek). You need a 400W PSU according to the 6670 requirements (source: http://www.amd.com/us/products/desktop/graphics/amd-rad...). I know you may be able to get away with less wattage but why risk it? The PSU may get fried and even if it doesn't fry the rest of your system, you will have to replace at least the PSU (adding to your headaches).
Here is a decent ATX sized PSU for the 6670 but you will have to go $10 over your budget for video card + PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Third, make sure that the video card length fits in your case.
Fourth, make sure that the case accepts ATX sized PSUs. I've seen many HP computers that only accept micro-ATX PSU sizes so watchout.
A Radeon HD 6670 DDR3 delivers at least 30 FPS minimum at 1920x1080 using the highest quality settings, and a better card gets you over 40 FPS. Even at 2560x1600, a Radeon HD 6770 or GeForce GTX 460 192-bit card maintains minimum frame rates above 35 FPS.