5DIII has way better focusing system than the 5DII. You will get better pictures with the III right away.
Not necessarily. Yes, the focusing system is more advanced on the 5D MK III, but like Tony Northrup showed, if you don't know how to really use the AF system, you can get poor results.
There is also a $2K or close to it difference between a 5D MK II and a 5D MK III
The OP has not told us what they are shooting, but if they do not need advanced tracking, then the AF on the 5D MK II may be fine as well as for the price of a 5D MK III the OP could get a 5D MK II and a 70-200 F/2.8 IS II, or pretty close to it.
And again, if their heart is for the 5D MK IV you will save far more money on the depreciation of a 5D MK II in the next 6 months than you will on 5D MK III.
Heck, if they do the right amount of hunting and show some patience they could possibly even MAKE money on the resale of a 5D MK II after they have 5 months of use which is a lot harder to do with a 5D MK III with the potential announcement of a 5D MK IV