http://pcpartpicker.com/p/rPzTGX
This is a pretty cookie cutter build. I got it from
ChooseMyPC with an added heatsink because the price on pcpartpicker is much less, your prices might be different.
Another good cookie cutter build for gaming/streaming/video editing like you want is
this one. You said your budget is $600 so I would add the
video card augmentation. Below that build on the same page is another build which is even better if you can cough up an extra $150-200 past your stated $600 budget. If you can, get
the same card in this build. I do believe you'll be extremely happy with both but I personally do believe the extra cash is worth it. However, we're not the same person so it's subjective.
I recommend the parts that @Ofu said above also but Intel/Nvidia is more expensive. The only reason to go with AMD/Radeon is price. If you have enough money, there is no excuse. Actually there is one excuse, Radeon cards are better for cryptography such as mining Bitcoin.
There are lots of ways to save money that people don't realize on top of this also. There are people that sell 100% legitimate and legal Windows license keys for very cheap. One such place is
softwareswap, which I see now requires an invite. One place that many people don't realize exists is Microcenter. They sell new 100% real parts for so cheap it's ridiculous. Very few people understand how they can do this. The only problem is that they are a brick and mortar store and don't sell very much online. However, you can find someone to buy the part for you at their local store and ship it to you. It's called proxying. Often times they work at Microcenter so they get it for even cheaper. One such place for this is
here. It's polite to leave a tip and pay for shipping but it still comes out much cheaper.