I got into Star Trek by watching random Voyager episodes whenever they happened to be on TV. It’s from the same era as SG-1 and is overall pretty close to what an “average” Star Trek show would be IMO. You can give it a try if TNG doesn’t click with you for some reason. Or go with SNW if you want something that’s currently airing with new episodes being made - every other “current” Star Trek show has either finished production or not aired yet.
One (small) issue is that it assumes there *is* a client outside of the server. Most server apps have both a web UI and an API, and it’s even possible to build an ActivityPub server with no client API at all (microblog.pub was like that, IIRC). I think the ActivityPub C2S API was intended for servers that worked just like you’re describing, but IDK if anyone ever really implemented it properly.