I have not played any of the Metro games, and understand that there are a few titles in the franchise.
Does Metro Exodus continue an existing storyline, or can the title be enjoyed as a stand alone game?
Games themselves continue (or build upon) a story from the book series Metro. Especially Metro 2033. You can and will enjoy this game without knowing anything prior, in fact, I'd say this is the best way to enjoy the world of Metro.
Metro 2033 book did this lovely thing where it presented you with an unknown, dark world and then threw you into it without as much as word of explanation. Half of the stuff in that book never is explained. Stuff that you could write a chapter about. Or make several quests about. The culminating point of the book remains unexplained. Writer doesn't tell us why, how or what lurks in the one particular part of the Metro system.
If you want to have a full experience start with Metro 2033 book, continue with all games in order of appearance. If you want to just play Exodus, you still will enjoy the heck out of it, I can guarantee that much.