OK this could be exhausting
First of all, Motherboard.
Probably, next to PSU, the most important part for me. Go for Intel 100 chipset. You wont do any overclocking as it would cost you additional CPU cooler, and i5 6600k is too expensive for you I suppose. So H170, B150 or H110. H170 is the best of those three, but some quality mobos could be over 100$ and again I suppose that not fits your budget.
I would go for B150 mobo over H110 because of more ports and B150 support PCI E 3rd generation where h110 doesn't among other, for me important things.
Now CPU
I picked the Intel Core i3-6100 over the AMD FX-6300 because:
- The Intel Core i3-4360 (same frequency, but older and lower performance architecture than the Core i3-6100) outperforms the FX-6300 in most games and applications, thanks to its far higher single thread performance, according to AnandTech.
- The Core i3-4130 (300MHz slower,two generations behind) outperforms the FX-6350 (+400MHz/100MHz Base/Turbo frequencies) when it comes to gaming performance, according to Xbit Labs.
- The Core i3-4130 has a far lower power consumption: 16W less at idle and 105W less at load! Lower power consumption = Lower utility bill, not requiring a more powerful power supply (saving money), less heat and less noise. The i3-6100 power consumption is similar to the Core i3-4130
- The Intel LGA1151 platform offers more recent technology, such as PCI-Express 3.0, M.2 slot, DDR4 support and more.
- The Intel LGA1151 platform also offers more interesting upgrade options with the more powerful Core i5 and i7 series of CPU. With the AMD AM3+ platform, you’re limited to slightly more powerful FX-83xx CPUs that are no match for Intel’s Core i5/i7 CPUs.
Intel Core i3 6100 is blazing fast processor, and you cannot find some important app that will squeeze it to the point it cannot handle. Of course, for example it would be good all around to buy i5 6500, but again , don't know if it can fit your budget. And i5 would be a better future proof as it has real 4 cores. Remember, in real world scenarios i3 isn't much slower than i5, except CPU intensive tasks, and on some synthetic benchmarks.
Like Dani mentioned, if you get powerful enough GPU, 95% of the tasks like video editing, gaming will be a GPU's job.
One more thing, if you at last want to buy GTX 960, it isn't really a need to go for 4GB model as it isn't a real bang for the buck. Both 2GB and 4GB models are too weak for any gaming or editing above 1080p resolution, but no important difference on 1080p resolutions. GTX 960 2GB model already achieves 98% of everything what 4GB model can do.