Charles Magnan

I'll tell you my three favorite starting points, that way you can choose if one sounds more your style!

Touhou 7 (Perfect Cherry Blossom): This is the one Eagle suggested! The second Touhou game for PC, it's a game that sticks to the basics, with great execution. The unique mechanic for this one gives you a temporary shield from time to time, as you collect falling cherry blossom petals during gameplay. It's not trying anything too fancy with its mechanics, it's fun to play, it's on the easier side for the series. And the music is incredible.

https://www.youtube.com/watch?v=AAdHRSUNZUs

Touhou 18 (Unconnected Marketeers): This is the one in the photo! It's also available on Steam (though you'll still want a fan translation).

The latest mainline release, it's evolved quite a bit since 7, but a lot of the changes here I absolutely love. This one has a kind of roguelite element to it, where you get to purchase an upgrade after every level. After your first time purchasing that upgrade, you can also select it as a starting upgrade for all future runs, giving it the most replayability of any game in the series -- and making you feel like you progressed even when you game over! Upgrades range from movement, survivability, additional attacks, etc.

I also really like the backgrounds and attack patterns in this one. All around, I think it's an amazing entry, plus the music is incredible.

https://www.youtube.com/watch?v=lgt072Jz2gY

Touhou 8 (Imperishable Night): Regardless of whether you start with 18 or 7, I suggest this one as your follow-up! Touhou 8 is terrific, but it's also got a kind of victory lap feeling to it -- with the largest playable cast, two different final bosses, etc. A ton of effort was put into this one and it shows, but I suggest playing it second because it might get you bad habits! The unique mechanic rewards you for sticking to either unfocused shots or focused shots for a while instead of adapting, giving you an additional continue if you were consistent enough during a stage. It's on the weirder side, but it's also a blast, its stage 4 has yet to be surpassed by any other game in the series IMO, on top of having the incredible split final stage concept and tag teams?? Oh, and the music is incredible!

https://www.youtube.com/watch?v=nmYnymCcKVw