Also, make sure you check that the GPU is supported on software that he'll use for acceleration. If he doesn't game, and the card wont support acceleration (or he doesn't need to), then get the cheapest GPU you can find (e..g 6540 or something) and spend the extra money on RAM.
No video cards won't become any cheaper.
My friend uses Vegas Movie Studio 10 on his PC with an AMD Phenom II X4 840 and 4GB of RAM and he has an ATI 5670 graphics card. Works well enough I guess but having another 4GB of RAM would help him I think (as well as a stronger CPU, but the FX-6300 has two more cores than his 840 and is a stronger chip anyway).
Not sure which edition of Vegas you're using (Pro or Movie Studio) but it looks like you might be able to enable CUDA support in Vegas 12, so it'd be worth getting the GTX 650 Ti if so. There's some information on it here: http://www.sonycreativesoftware.com/vegaspro/gpuacceleration
I don't think anything older than Vegas 12 supports CUDA, so in that case you could get a cheap Radeon or something like Okedokey suggested.
Well you're gonna need to get an AM3+ motherboard whether you go for the FX-6300 or the FX-8320, because an AM3+ CPU won't physically fit into the FM2 socket which the board you linked to in your first post has.
Try to get one with a 970 chipset if you can, but really any AM3+ board from Gigabyte, MSI or ASUS will be fine with the FX-6300 or the FX-8320.
Yeah that'll be fine so long as he's happy with the mATX form factor. Are there any ATX AM3+ boards in your price range? You'd only buy mATX if you wanted to save space and house the board in a little case.
That motherboard is fine, just make sure you update the bios.https://www.asus.com/Motherboards/M5A97_LE_R20/#support
No that PSU aint that great. Get something like this instead... http://www.newegg.com/Product/Product.aspx?Item=N82E16817139049
The board you've got is good, so don't exchange it. Case wise, I'd go Source 210 or Z11. See if the Corsair 200R is within your prince range. That's a nice little case. It might only be mATX though - can't remember. You'll need to check that.