All of your parts will work together, but I have a couple of suggestions.
A 750W PSU is overkill, 650 would probably suit you just fine. You might consider
this XFX 650W PSU, which is $90, but has a $30 MIR. If you're set on the 5770, there's also
this combo, which offers the XFX 650W PSU with a 5770 for $200 - $50 in MIRs...$150 for your PSU & video card together is pretty good.
You might consider spending about $20 more for a new 6850, rather than the last-gen 5770.
Powercolor and
HIS both have cards for $180.
Your OS link goes to the Seagate HDD again, I'll assume that you meant to link Win 7 Home Premium. If not, do you really need Pro or Ultimate? They offer very little for the average user.
Do you have a DVD burner? Any SATA DVD burner will do, don't worry too much about brand.
In theory, you could spend $15-20 more and get CAS 7 1600 MHz RAM, but the real-world difference is not likely to be noticeable.