So that’s a very hard question to answer as, while the genre did keep most of the basic concept, every game had its own specialty.
And to really reassure you : every game has a very thorough, complete, crystal clear tutorial to help you understand every game mechanics.
From a certain point of view I’d say “play them all in the release date order”. You can very easily get all of them for cheap during sales.
But from another angle, that’s very redundant - while still being pretty awesome, I’m a sucker for complete series😎- because as Creative Assembly (the creators) made game after game they never stagnated and every game did improve on the formula.
To avoid writing an essay or bore you to death (which in retrospective I might still have done) , I’d say according to your preferred era (it does play a very strong role in how much you can immerse in the setting or even be proficient as many features are historically relevant if not outright correct) pick the second title.
I’ll explain : Shogun was the first and awesome (I had it ORIGINAL back in the day) but you can see how it aged poorly. Scope, graphics, playing area, and overall grand strategy layer are all crippling small - and to be fair Shogun 2 gets to be one of the most awesome titles ever. Improving on literally everything without a single fault.
Medieval? Same story. I bought the first with its expansion when it was released as a bundle and went full crazy for it. Beating it twice. Hundreds of hours spent on it.
But the second it’s overall much better, even if a multi-hundred-hours player can see how a little amount of minor changes didn’t necessarily improve things. A new player would never notice them which makes it a perfect game to start with too.
Rome or Rome 2? Same discussion.
With Empire and Napoleon it gets harder to tell. Pick both - while having a common timeline they offer very different things and vastly change the entire game feeling.
Then you have weirder titles like the three Warhammer fantasy which are all extremely worthy! But again, the main thing is : you have to love the setting.
Mind you - up until Empire there was no 3D ship battles, just statistics of how the two forces faced each other. The more ships you have (or the better ship’s quality/generals) the higher the chance of winning. With Empire, and the title following it → Rome 2, you can choose to managed also sea battles in 3D.
And in any case every game allow you to just concentrate on the grand Strategy layer and leave 3D battles to the automatic resolution (which is not totally random, it does fight well, honestly). You always have the chance to save before every battle so you can also cheeky your way out of things and so on.
Extra credit : If you want to completely give up on any form of social life/interactions you can easily check ModDB and see the absolute mind-boggling amount of mods (FREE mods) that have production values equal if not superior to the actual released game. But if you want to push realism don’t miss the Darthmods. They are the pinnacle of Total War. I am not kidding. That stuff is superb, perfect, extraordinary.
Empire is a staggering better game (and also you can tailor it to your needs so minutely) with Empire: Darthmod.
It does not just add units, it literally fixes sensitive areas of enemy AI, bullets behavior, and both strategic and tactical level.
But you will find (mostly for Medieval 2) total conversions for Lord of the Rings settings, Game of Thrones, First world War, the obvious Star Wars stuff, and much much MUCH more.
In short : any game you will pick will do its very best to charm you, I promise you that. But honestly you want start playing something that speak to you in a very personal way in historical terms.
If you have only a passing knowledge of the period you might feel overwhelmed or unconnected which is a shame.
Personally, if you haven’t played Medieval 1 and 2, Rome 2, and Empire you are really losing on some of the best strategy games the world has to offer.
And that’s without even beginning to touch the Multiplayer : competitive, cooperative, skirmishes, historical, and so on…
But that’s just nerd me.
Edit: sorry for the typo, got cramps while typing on the phone. Will correct them gradually.
Edit 2 : Wheeew, done. Sorry for the wall o’text, but I couldn’t honestly have written any less. If you have any other questions at all feel free to ask. I must have over 3000 hours in all games combined. If I know an answer I promise I will answer.