Hmmm, light gaming does not necessarily mean games that are light on resources.
Build II ruled out for having no graphics accelerator card, the Intel on-die doesn't really count as any better than a display card.
Between the Athlon II and the E5800 I would go for the Athlon II because it's the more powerful of the processors, but I cannot outright recommend Build I because I'd be looking for a minimum of 4GB of RAM.
What's with the "P.S."? It implies that the final spec for Build III will be different from what you posted.
Actually build 2 is a Sandy Bridge dual core - vastly superior to the old Core2 Duo. Gaming really will need to be 'light' though with the graphics muscle you'll have to play with (or lack thereof). For non-gaming purposes a G630 is a modern, quality CPU that will serve you well.
By the way, don't base your decision on the processor's clock speed - that's a really inaccurate and outdated way of doing things. Even 10 years ago there were Athlon XPs outperforming Pentium 4s despite having significantly lower clock speeds.
EDIT: And what's said about the graphics in build 2 is correct, but only in that the integrated graphics are hugely inferior to modern cards that aren't rock-bottom budget end. The 6450 you're looking at there really is rock-bottom budget end though, so there's not really much difference there. Check out this chart:
Build 2, without a doubt. 6GB is an interesting quantity of RAM though? I'd say stick with 4GB, but with memory being so cheap, I guess it won't have much impact on price anyway. With the motherboard you've chosen, you could always add in a more powerful graphics card at some point in the future.