Best CPU for streaming/recording MMOs?

i7 would be a best choice, the 2600K would be the most reasonable choice.

I'm willing to spend up to the price of an i7-3770K, I just need to know how it outperforms the other processors. As an example, I noticed that its L3 Cache was smaller than than i7-3820. What does that mean exactly? Is it still a better processor for what I'm looking to do?

I would go with the 3770k. HT will help with the software-encoding and you will be ready to use IB QuickSync (which is twice as fast as SB's) if the streaming software ever implements support for it.

With QuickSync-capable software, IB CPUs are the fastest transcoding solution on the market today.

When it comes to multitasking the benefit of hyperthreading is apparent and it's much better to have 8 threads then just the 4 cores. Intel i7 cpus have hyperthreading and the i5's do not. So based on that I would rule out the i5's.
Then that would leave the 3770K , 2600K . 2700K and the 3820.
The Ivy Bridge s a low power cpu and was designed for functioning on only 77w TDP , but because of that low power design it hasissues with overclocking and heat.
The cpu will overclock but when voltage is being added at the higher speeds there is a bigger amount of heat relaesed from the cpu that has to be dissapated and higher costing heatsinks or water cooling is required.
The Sandy Bridge cpus are much better overclockers so that will give you a better chance of reaching your target overclock without heat being too much of an issue. These cpus are not without thier limitations though and the Pci-e bandwidth lanes are few and that means in the video card department your limited to two cards running at x8 bandwidth each. If the video card issue is a non issue then these two cpus are good to choose from and the 2600k has been a popular choice lately.
The last choice on the list is the i7-3820 and it's massive video bandwidth , the Sandy Bridge-E processors have 40 lanes of video bandwidth and that means you have two video cards running at x16 and the third at x8 or four at x8 , plus it does have hyperthreading and can be overclocked to a preset point since it's not a K model it can't go as far as the 2600k. The motherboards are a little more pricey because of the added features that the cpu supports , and the maximum ram it supports(64 gb).
Hopefully this is some more info that can help in your choice of cpu and you'll have to consider what the options you want are.

Alright, so I suppose I'll stick with the i7-3770K. Now, about motherboards....

I'm leaning toward the ASUS P8Z77 series, but man, there are so many stinkin' options. What sets them apart aside from the occasional extra PCI-E slot??

I think motherboards have always been the one thing I've never understood fully. So many varieties, but they all seem so similar. Would anyone recommend a better, but similarly priced, series of motherboards? Which of the ASUS P8Z77 is the best bang for the buck? I'm willing to spend up to ~$250 on a motherboard.

Oh, also, don't some of them come with that nifty little OC button nowadays?

The reason why motherboards based on the same chipset have nearly identical features is because the majority of features are provided/defined by the chipset and CPU so there is little for board manufacturers to distinguish themselves there. Each new chipset generation integrates more features than the previous ones and reduces the number of extra chips needed to round up the core feature set most people are likely to ever use.

Today, the only optional IO chips a motherboard still needs to round up its core feature set are audio and network since those analog circuits are too sensitive to easily integrate into a noisy/busy chip.

Things sure have come a long way from the PC-XT days where the only integrated "feature" was the keyboard controller.

Ah, good information, and nostalgic as well!

Any recommendation on which motherboard I should focus on? What do you think of the series I referenced?

I personally have not had any problems with Asus' boards and something in the p8z77 series would be near the top of my list for best balance between features (I personally would be going for the more basic versions like the LX since I do not need any of the extra IOs on more expensive variants), reliability and price.

If your looking for an easy small overclock then the Asus boards are someting to consider. They have preset overclocksettings and all you have to do in the bios is select one and save and exit. They may have changed just a bit with the newer boards but the presets would take you to something like 3.8 ghz and then 4.2 ghz. I had the Asus Rampage Extreme 111 with an Intel 980x cpu , in the bios I selected the AI Overclock option and then cpu level up. From there they had two choices crazy @ 3.8 ghz and crazy @ 4.2 ghz , I chose the second one at 4.2 ghz and saved and exit and then my cpu was overclocked to 4.2 ghz and stable.
The Asus boards are user friendly and very easy to use and full of features.

ASUS P8Z77-V LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
$179.99
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

You don't have to pat $250 to get a good board and for $180 you can get one that will be good enough.

ASUS P8Z77-V PRO/THUNDERBOLT LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
$249.99
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

If you did however want to spend the $250 on a board then you could go with this one and you'll probably ask what sets this one apart from the other one. The new technology called Thunderbolt is what will do that. Think of it as a super beefed up usb that can also be used to connect to a monitor for video. You can daisy chain the components so that you only need one port and at the end of the chain would be the monitor. Apple computers have had this technology for a few years now and it's finaly coming to the Pc. But this may not be something you want right now but it's what makes the board a bit more expensive. Plus it has built in wireless lan.