"Raw" ususally refers to uncompressed video (though this is technically wrong), meaning you probably have a very large file. Rendering is the process of re-encoding the video using another codec, usually to reduce file-size while maintaining a decent enough video quality. The reason that .mp4-files with the H264-codec are widely used is that they offer a very good filesize-quality-ratio.
In your case, a very compressed file is not what you might want, since Youtube reencodes your video when you upload it. Every reencoding reduces the video quality, so the double reencoding will result in poor quality.
If you cant upload the .ts-file directly (I don't think Youtube allows this), you could reencode it to an mp4 or avi (imho, the latter is better in this case, though getting the encoding settings right is a bit tougher for beginners). The key is to chose a very high bitrate and the same framerate and resolution as the original video. Using a high bitrate, the quality-loss resulting from the reencoding can be minimized. However, this will result in very large files (espacially if you choose avi), which depending on your internet connection might take very long to upload.
There is a range of free encoding programs out there. I'd recommend XMedia-Recode, but you could also try Xilisoft Video Converter or Format Factory.
Edit: If you want to cut your video (i.e. add an intro and an outro, put different videos together, remove unwanted parts, ...), you'll need a video editing program. There are some freeware programs for this (none of which are as good as professional, paid programs), you can find a list of video editing software at wikipedia.
apt-get install mediainfoon Debian/Ubuntu.) The MPEG-TS container format can hold multiple different formats. If it's just the same h.264 stream that your desktop encoded and sent to twitch (so there haven't been any lossy re-encode steps), and it's not too big a file to upload to youtube, then just upload it directly. Or remux it to an mp4 container (without transcoding). I assume there's a gui for this, if you don't have command-line