I have a drama that maybe doesn't neatly fit into one or more of these story types, in the sense that I've been wracking my brains to try and find a "X meets Y via Z" type logline. I guess if you're a top writer like Aaron Sorkin, then you can do what you want. But for a first time writer, how important is it to fit your story into one or more of these categories.

Pliny, if the story works, it works regardless of genre. The main value I see working with genres and story types is more front-end of the process -- brainstorming, plot and character development, keeping the writer on target during the writing process. Once the story is pretty much set or draft is written, probably less value in squeezing a story into this genre or that. However if a writer has a script that just isn't working, perhaps a genre switch can help. As we noted in our analysis of Good Will Hunting, it started out as a spy thriller before Rob Reiner convinced Damon & Affleck to turn it into a drama.