Running a 24/7 radio station on YouTube or a "Sleep Stream" on Twitch? You don't want to leave your PC on all day. An RDP server is the perfect solution. You can run OBS Studio on the remote server and stream continuously.
By default, RDP is not great for watching video, but it works perfectly for sending video via OBS. The server encodes the video and sends it to Twitch's servers. You don't need to see the smooth video on your local screen for it to work.
OBS Studio is the standard. It runs fine on Windows Server. Just make sure to install the "Desktop Experience" feature if your server doesn't have it enabled, otherwise some audio features might be missing.
RockHoster's Elite VPS (4 vCPU / 8GB RAM) is powerful enough to handle a 1080p stream using CPU encoding (x264 fast preset) without dropping frames.