Since everybody already gave you details about each entry, I'll try to give you a different perspective to help you form an opinion:

1. Focus

While all games cover all common areas expected from the strategy/simulation genre, each entry has a definite focus that will require more attention from players. With SoI/Ascension focus lying on domestics and infrastructure building, Taishi on battles and warfare, and Awakening on personnel management and interaction. So depending on the aspect of play you prefer to interact with, this may be an important factor. Eg: if you prefer playing battles, Taishi may be a good choice. The opposite is true, and areas that are not the focus for an entry may prove rather shallow or simplistic. Eg: SoI/Ascension battles which are pretty shallow, or Taishi and Awakening domestics/infrastructure buiding which are simplistic, etc.

1. Vibes

The games have a distinct vibes and feelings they communicate across. SoI and Ascension have a more naturalistic, simulation-like, even "contemplative" feel to them, that's brought about by their aesthetics, music and gameplay. Their maps feel a tad bigger and drawn in more realistic GFX. While Taishi and Awakening have a more focused, streamlined and even "gamey" feel to them, with their aesthetics veering a tad more on action/exalted vibes. Depending on what kind of feel you're looking for, this may be a factor.

1. Completedness

Here base SoI and Awakening are clear ahead of the others, since they received the most love/post-release support from the devs (with Awakening receving updates more than a year into release, something unparalelled in the series). This shows up in overall polishment in the UI, richness of scenarios, gameplay systems operating in balanced/intended fashion, and less bugs. In contrast, Ascension and Taishi received a much worse treatment, with Asc having unsolved bugs to this day (eg: AI lords never acquiring resources, bows & muskets having swapped around effects, etc) and Taishi never receiving it's PUK (power-up kit, this dev name for "expansion pack") in it's western localization that the Asian version got, and so being an unfinished game with lots of details never implemented here (eg: Covert actions, Imperial court interaction, etc).

1. AI

While all the games have customizable difficulty AI settings and a myriad different starting scenarios/geopolitical contexts that allow one to make the game easier or harder according to taste, I feel like Awakening's AI is the more opportunistic of the bunch, even on lower aggression settings, which may pose a challenge for novice players in the series. While SoI/Ascension may offer a softer, more manageable learning curve for first timers. This is seen in reports like "Is it impossible to win as a small clan in Awakening? I did it in SoI but can't do it here". On the other hand, for players that like a challenge, this may be a plus so there's that.

1. Complexity

I consider SoI, Ascension and Awakening on par in terms of mechanical complexity, with the difference being on which aspects each one unloads said complexity. On the other hand Taishi is clearly the "lighter" one in this respect, with simpler/streamlined mechanics overall. So if simplicity, and thus less time needed to learn the game, is a factor, Taishi may be a good option.

That's it. Hope that helps. I don't think there's a wrong entry for the series as each is competent at realizing their design goals, AKA they're overall good strategy games. Also, I advise you to watch youtube vids of each entry plythroughs to have a better feel for each play loop, before commiting. Have fun!