I have a middlin' 34" ultrawide and stream at native 2560x1080p using the NVENC encoder. At the maximum twitch bitrate, it uses <1Mbit/s and any scaling issues are avoided. Yes, people with 4:3 aspect ratio screens are going to get black bars, but that's their problem. I don't stream for money and can't be arsed about subs and bits and whatnot, but it's something to keep in mind if you have a commercial interest in it.
I specifically got a 1080p monitor because I wanted to dual-screen with my old 27"er, but it turns out the setup is just too wide for the nook where I sit. I /should/ have gone for 1280 or more vertical pixels in hindsight, but I can live with it. Needless to say, I could never return to a smaller screen size for FAF, the increased viewport is just so much nicer and improves your situational awareness.
One problem I did have was that the default UI layout is not workable for me - the resource bars at the top left are basically out of your ocular angle and you don't even see it flashing red. MovableUI mod sorted that out for me, I now place my stuff towards the center of the screen and it works well. Even though the mod has some issues, I couldn't go without it even on a smaller screen I think.
Oh - I'm using a GTX970 for playing and encoding and it's powerful enough even at the highest quality settings I can configure. My bottleneck is my processor really - I only have 4c/4t and would recommend at least 4c/8t for creating a quality stream with overlays and allsorts.