FriendlyFire said:
Shogun was great but shows its age now
MTW also good but found it a little sameie
RTW big leap forward.
RTW: BI is not bad
RTW: A is not worth getting
Shogun Total War: great at the time, only played the demo so I wouldn't really rely on my opinion too much here.
Shogun Total War: Mongol Invasion: Never played it, never heard any reviews from credible friends (or any friend-based reviews for that matter).
Medieval Total War: Good, kind of low on the graphics side of things, but all in all still pretty decent.
Medieval Total War: Viking Invasion: Never played it, but from what I hear, trying to fight off the Vikings early on is brutal (according to a friend, they come in great numbers, and well equipped).
Rome Total War: Much better Graphically, a whole host of cool units. Very annoying Senate, and there is a tendency for enemies to brutally gang up on you. Not too hard to deal with, but still a nuisance.
Rome Total War: Barbarian Invasion: Didn't have the cash, so I downloaded the Rome Total Realism Mod. That added a whole host of new factions (a good mix of "civilized" and "barbarian" factions), new units, and removed the annoying Senate. RTR satisfied my need for more barbarians.
Rome Total War: Alexander: Again lacked the proper fiscal surplus required for the acquisition of this game.
Medieval Total War 2: Most visually appealing of them all. If you've got the computer, get this game! From what I've seen it combines the visual aspects of RTW (on steroids) along with timeline of MTW. Can't do much better than that.
I hope this helps somewhat. But despite what we say, take the one that appeals to
YOU most.