Medieval 2 is the best in the series IMO, if you can cope with the slightly dated graphics. It has scope and variety, but at the same time it has most of the features that the series accumulated through time. It has also aged fairly gracefully and plays well even today.
Shogun 2 has the most refined mechanics and great presentation, but lacks the scope of earlier games in the series, as well as variety in playable factions. Namely, you get to play the Japanese, with the actual differences between the clans being microscopic for the most part. However, the it's a well crafted experience that I'd put in second place.
Empire has some cool concepts, but the ranged combat it focuses on works poorly in the game's engine. Also, there are some cases of poor balance in the campaign (England, Spain and France getting their colonies automagically, Maratha always winning in India and becoming borderline unstoppable, etc.), but it's still a solid game, especially if you are interested in the time period. I'll put it in 3rd place.
I'm sure a lot of people in this thread will say Rome, but by this point the game is showing its age. It feels a bit featureless compared to the later entries in the series and the graphics are quite dated. However, it was the best Total War game at its release and is wort taking a look. I'll let it share 3rd place with Empire.
Shogun and Medieval are VERY dated by now and are both superseeded by their respective sequels. They should only be considered for nostalgia or historic value.
Napoleon is poop.