I have installed an XFX 550W Core Edition Full Wired (Bronze) - P1-550S-XXB9 in an HP Pavilion. It's quieter than the Delta Electronics OEM power supply that was originally in there. It's also made by Seasonic for XFX.
I have similar HP cases - they are all slightly different. Take a tape measure and see how much room is available. The card is 9.49" (length from the back of the case to the tip of the card) and 5.39" (height - this shouldn't be a problem) x 1.67" (wide - this shouldn't be a problem either).
The PSU is a standard size...they are always a little snug, but they fit.