I did this for my friend, same res I got him a biostar h55 and an i3 540, CM212+ and a 6870 and some cheapo ram. (reused an old case and psu)
btw if you need a cheap 5770 i got a new one for sale
Edit: DDR3 is dirt cheap so i don't think that will be an issue for you.
Alright well we're also going to be borrowing an old hard drive due to the current prices. So that's not an issue.
So far we have the:
gpu (maybe unless i get other recommendations)
any other ideas?