No you cannot put ddr2 into a ddr3 slot, you could put that memory into the first system to give you 8gb
A 2nd build like the first would be fine, infact you could probably go for a lower cost motherboard like the gigabyte GA-MA770T-UD3P
It's only the 770 chipset so no crossfire but with a single 4870 that's not really an issue.
I'd also consider the Sapphire Vapor-X version of the 4870 it's a very good cooler and is probably a bit cheaper
Cannot say much more on costs as I don't know what it's like in the US, execpt for occaionsally looking at newegg and then I ignore the prices as the price differences can diver me mad.