Whoo boy, having played them for thousands of hours and even working on mods for some of them, this is a difficult thing to answer.
- Rome Total War
The one that got me into the franchise. The time it came out I had tried out the demo where you play as Hannibal. This demo made such an impression on me, that I continued to play the game for 3 years solid every weekend and some schooldays.
It was this demo: https://www.youtube.com/watch?v=203P0lBzqGA
- Medieval II Total War
Crusades? Mongols? I mean come on. It was fucking awesome and fully improved upon previous iterations. I love all its expansions. Especially the Teutonic campaign was incredibly fun. NA'AM SULTAN!
- Empire Total War
This was the one that really got me deep into it. So deep that I started making mods myself. Portrait/name changes, new units, colour corrections and some texture changes. My god I loved it. I also loved the American Revolution angle to it and how it was a big big campaign map.
- Napoleon Total War
This came out in a period where I got really into the whole French revolution leading up to the Napoleonic wars. Played for thousands of hours and again working on mods. To be fair, this game is best with some of the mods out there that frees up more factions in campaign.
- Shogun 2 Total War
Criminally underrated game, it got especially good during the later turns of campaign when more modernized weaponry are introduced. Kinda gave me hope for a possible WW1 game. Also, who wouldn't choose the Satsuma clan with their Triforce flag?
- Rome II Total War
Pretty crappy launch, missing family trees and lots of bugs. Kinda lost faith after this one although... I did revisit the game a year later when they had finally fixed most of the problems I had with it. After that had a blast with it.
The rest... I kinda lost interest because the settings didn't do much for me. I like Warhammer but honestly I like it more for space battles and whatnots. The newer ones.. same thing. Not interesting in the era.
Liberate Hong Kong, the revolution of our times!