You need to know there are differnt versions of the 560 ti,
a 1gb/2gb model with 384 cuda cores, and a 448 cuda core model.
*IF* you go this route dont buy the 384 models... not worth it, compaired to the 448 ones.
That means you need to spend like 250$ for a 560ti.
You can find a 7850 for less than that, and it has better overall performance before you factor in overclocking.
So in short, dont go for a 560ti, not as good value compaired to a 7850.
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On another note, dont get a Phenom II x4 965.
I believe if you can find a FX-4100 in same price range that is a better buy.
the FX-4100 is slightly faster than a i3-2130 in benchmarks/gameing, and it has overclocking.
Its not uncommon to be able to turn off "turbo" funktion and hit 4.6ghz with these CPU's.
So for a budget build that doesnt mind overclocking the FX-4100 is good value.
Get the cheapest motherboard you can get away with

as long as it has the features you want it to have.
Bulldozer FX-4100 @ 4.6ghz 7/24 stable (most seem to hit) > Phenom II x 4 @4.0ghz (not as many hit)
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CPU cooler:COOLER MASTER Hyper 212 Plus ~29$ = insane value buy.
I can HIGHLY recammend this cooler, its performance is superb considering its price tag.