It has the fastest drive and the best video card of the three setups.
Say for instance...
I want to buy the second one.. and then buy I really good graphics card to put in it afterwards. Would that work out better?
... Why would you buy a premade one just to replace the stuff in it?
As for your i5 & i3 vs AMD question: keep in mind that the AMD is a quad core. I think those i3 and i5 computers you linked to are both dual core types.
So, out of all of those you linked to, spec-wise the first one is probably the best.
I don't understand the time and not money thing though. You realize that time=money, right? What you save in money will save an equivalent unit of time that it took you to make it (in some way), which can probably be used to build that computer. >_>;
Well, unrelated time/money stuff aside: as far as building: as long as you know how to screw screws in and connect a few cables, you can easily build a computer in a period of some hours. Start it up, install an OS (you can do this unattended), and then install some drivers. Once you get it running, that time you invested making it will never have to be spent again. It's a one time investment, and it's getting easier and easier. You would probably spend longer looking for the parts, but that's about the same as the amount of time you'd spent looking for a prebuilt one that would exactly suit your purposes.
Which are gaming and blu-ray. You need something that has good graphics capabilities and a blu-ray drive, specifically. It really depends on how much you want to game, and how much you want to watch movies...