Never played Onimusha
Is the first game cool?
I've played 1-4. So basically all of them. They're a mix of combat (and accompanying resource management), puzzles, a little exploration, and unique to the fourth (and best) game mainly, secrets and RPG systems.
First game: Samurai action-adventure with a splash of Resident Evil...but not good. The combat is basic and not particularly challenging, the secondary gameplay elements are not...in their element yet. Some OK puzzles. Bland music. OK at best level design. Stylistically it is cool as most capcom games were back then, but it was no match for Resident Evil and Devil May Cry. Every aspect of the game feels like there's something more missing, but it's not bad.
Second game: probably the most representative of the first three games. Samurai action adventure with a little more of a complete vision and higher production values but still ultimately not that good. Close to classic capcom quality, but not quite. I would recommend maybe playing this game as an intro if you don't mind it not being a top-quality game (7.5/10 maybe?), then jump right to 4.
Third game: Stars a french actor, time travel and is half set in modern day france, half in fuedal japan...because why not I guess. It's a toss-up whether this or the second is the best of the original trilogy. Production values are higher once again with some pretty stunning cutscenes and levels. Gameplay is barely changed from the second game, but there's minor improvements and additions. The main difference is two distinct playable characters but this only injects variety, not mechanical or systemic depth. Better than nothing changed nonetheless.
Fourth game, my personal favorite: production values (budget) is reduced slightly from the third game, or at least it feels that way as there's less crazy pre-rendered CGI, and the overall more serious tone of the first three games is dropped a little in favor of charming Japanese goofiness at times, but gameplay-wise it's top-form for the series with more on offer than ever before. Fairly extensive RPG systems, 6 playable characters make up your party to build, and actually executed in a fun and enjoyable way (rare for action games), puzzles and secrets galore with the puzzles being more interesting than ever, decent level design mostly, a pretty good soundrack I think as a series first (I don't remember a single track from the first 3 games sticking with me). lots of bossfights...the only catch is the second half of the game devolves into chain critical hit spam unfortunately. Though this does not apply to bosses at least. A solid 8/10 and one of my top ten PS2 titles. And most overlooked. Release date was 2006, when the next (awful) gen of consoles was now the focus.