The 2600K is essentially the best gaming CPU you can buy. It'll chew through Battlefield 3 with ease. The limitation will be in the graphics card. You may even want to downgrade to a 2500K and use the $100 difference to buy a more powerful graphics card, but that's up to you and it depends on your budget constraints, etc.
Sandy Bridge is also the
best way to transcode video, so that will really help you if your video editing software supports Quick Sync. However, to use Quick Sync you need a motherboard with a H67 chipset (as opposed to P67), which doesn't support overclocking. Or you can can get a Z68 based board which costs about $10 more than a P67 one, allowing you to use both Quick Sync and to overclock the CPU.
I'm not a fan of overclocking, personally, but Sandy Bridge actually overclocks extremely efficiently, and it's something I may do years down the road when I start feeling that the CPU is getting too slow for what I need to use it for... so it's a nice option to have.