This is an area where the answer isn't clear. Any CPU can handle Vegas or Premier, but the time needed for encodes scales well with core count. Despite the Pentium having vastly better single-threaded performance, either an 860K or FX6300 should beat an overclocked Pentium in those programs.
On the other hand, many games like single-threaded performance and don't scale all that well with core count - though most will benefit from up to 4 threads. Minecraft should run fine on any of the above CPUs but the Pentium will theoretically deliver the best FPS in a heavily modded game. Single player games and those with smaller budgets will run better on the Pentium (Guild Wars 2 may be 60%+ faster on the Intel chip), while AAA online multiplayer games will run best on the FX6300 since the studios have enough budget to code them so they scale with many cores.
I'm reluctant to recommend a dual core today since so many programs/games scale well to 4 cores/threads, but there are plenty of members on here who are very happy with their Pentiums and will probably give it their vote. The FX on the other hand is on a very old socket with slower USB/SATA/PCIe and worse onboard audo/LAN solutions, and though these are generally minor details, it adds up. The Pentium and 860K will be cheaper than the 6300, giving you more budget for a better video card or a solid state hard drive, which makes a huge difference in day to day usage. Of those three choices, I'd probably vote for the 860K and recommend you overclock the snot out of it.
A little up the foodchain is the i3 which should be the best of both worlds, but it'll eat more into your budget for other components.