Well, what are you going to be streaming?
----Casual----
If you are streaming something like making cookies, or i've seen people streaming themselves drawing for example, you can get away with 4GB of RAM and a few different apps for viewer counts music, whatever. But note Windows 10 can chew right threw 4GB fairly easy so with 4Gb keep the browser tabs down to a minimum, 720p 30fps should be very doable if all you are doing is using your webcam and talking. The CPU isn't as important, but its still has to be able to handle rendering, you can get away with a old i3 if you are going this route.
----Gaming----
Now gaming well, I like to say 16Gb will pretty much allow you to stream even the most demanding game, thats if the CPU can handle it of course, tho you can get away with most games with just 8GB. I like to look at the system specs of the game, if the game requires 4GB of RAM, double it to 8GB if you want to stream, if the game recommends 8GB Double it to 16GB for optimal performance, that goes with pretty much any game.
Though you have to make sure you're CPU can handle playing a game you want, and is able to handle streaming, If you have a GPU newer than a GTX650 or GTX750 you got the option to use Shadowplay or (NVENC in OBS or other streaming software) which will use the GPU for the rendering and allowing the CPU to breath for a smoother experience. Of course more cores and threads higher clocked the better.