First of all I don't think that you can put at all an AMD card because your current motherboard has an nVidia chipset, so you can only use nVidia cards.
Second your mobo isn't ITX it's standard ATX, so it will fit in most cases.
Now as for your case and PSU, I would recoment Thermaltake. A simple case with window costs around 35$ with 4 or 5 case fans. As for PSU if you aren't planing to go CrossFire a 750W PSU is too much and expencive.
Case: Thermaltake V4 BL edition
PSU: Thermaltake M550W (550W the HD6670 needs at least 400W)
Thermaltake Level 10GT-ToughPower 1500W-Frio Extreme/Asus Sabertooth 990FX/AMD FX 8150/Asus HD 6990/Kingston Hyper X Predator KHX18C9T2K4/16X /WD VelociRaptor 250GB(Main),x2 320GB(Raid BackUp)Caviar Black,2Tb Caviar Black x2/Creative SB XFi 3D Pro/LG Blu-Ray x2/Windows 7 64bit/Samsung T27A950 x3/Samsung HT-D6750W/Logitech G19,G9x,G13.