streaming video_ts files

I doubt there is any way to do that from the iMac G4 (which I suppose yours is, the 20" 1.25GHz model, nice one!). The software, which I guess on yours would be OS X 10.5 Leopard or 10.4 Tiger. Both operating systems came out in a time where watching movies on a TV would be from a DVD, and streaming really was in its infancy. The operating systems really have no streaming features build in, which is already prohibiting. Plex Media Server has never really supported PPC, there are old Intel versions that have a PPC executable inside of the .app file, but again, they're old and might not work very well. It was discussed in this thread, you'll find a Web Archive link to find old versions of PMS, and they discuss in detail how it works in the thread, it's worth a read: http://forums.macrumors.com/threads/plex-media-server-ppc.1529237/
But you might be more interested in getting a cheapy old C2D machine, either Mac or PC, and run a modern version of Plex on that, and just have a second drive for streaming purposes as well. I don't want to discourage you, but the reality is, is that these computers come from a different era, and you need to keep your expectations to such a level.