I come humbly asking for guidance: Whats a good Touhou game to start off with? Not for a total newcomer to shmups, but for guy who kinda knows what he's doing and has played an unhealthy amount of cave shooters.
everyone always likes to say Touhou 7: Perfect Cherry Blossom is the best one to start with, and I'm not here to disagree with that. it's got some of the most recognizable music & characters in the whole series in it, and the final boss has one of the coolest "oh shit!!" moments featured in any of these games. the character shot types are all pretty simple and easy to understand, and the scoring mechanic of the game is centered around the Supernatural Border - a shield that activates from collecting little sakura leaves that can either take a hit for you, or you can dispel in order to clear all of the bullets on screen. it gives you just a little more longevity in a game that already gives you lots of lives; it isn't necessarily easy, but it is friendly.
if you have shmup experience though, you may not necessarily want to seek out the "easiest" one. Touhou 6 - The Embodiment of Scarlet Devil is definitely more unforgiving but this is also by virtue of it missing some crucial quality of life features that debuted in the next game. but it's a game with equal character & music recognition. conversely, Touhou 8 - Imperishable Night is one of the best, most consistent games in the series, full-stop. it's immediately more difficult than 7, has weird and fun shot types, and has the "i think that im touhou" song in it. but ultimately might be a strange one to start with in that it may teach you bad Bombing practice: the game gives you a LOT of time to hit the bomb button to save your life after getting hit (at the cost of two bombs) that the other games do not afford you. all in all, 6, 7, and 8 are all good places to start, for different reasons. they feel like the "golden age" of touhou to me.
if you want a total wild card answer or want to try a more recent touhou, i recall Touhou 16 - Hidden Star in Four Seasons being really approachable, too. it seems to revisit/iterate on some concepts from Perfect Cherry Blossom that make it feel easy to pick up and play! similarly, Touhou 14 - Double Dealing Character was a blast and an attempt to "return to form" in the series after a stretch of more complicated games.
sorry that's not a very simple answer, but i hope this helps! i think these games get a lot of reputation for being Very Hard, but while they aren't Easy games I certainly think there are some that are really approachable and easy to understand such that anyone can pick it up and play on Easy or Normal difficulty and have a really fun time!