I really like doing the same thing, Brasky-- find a series that people say is awesome but finished, and then get the entire thing on DVD and watch it over the course of a weekend (or multiple weekends, depending on how long it is). We did that with both Firefly and Deadwood. Both are absolutely worth it.
Firefly takes place on a spaceship and involves all sorts of futuristic technologies, so technically it IS "sci-fi," but Star Trek it definitely ain't. Don't let the space aspect put you off, as it's mainly just a setting for a story that could take place anywhere.
The word I would use for Deadwood is "gripping." There are places in it that are very fucked up, and one episode in particular that I just wish I hadn't watched, but every single character in it is priceless. (Developing a minor crush on Doc Cochran didn't hurt)