RE: Lyric Hartwell

Game-wise there's a few good starting points, I'm gonna go with the easy answer everyone does and say Touhou 6 ~ Embodiment of Scarlet Devil. It's where a very large chunk of the big popular references and characters come from, it's not Too hard to be a first game (not easy, but not like LoLK or UFO hard)

After that, honestly just go to whatever seems right for you! Do you wanna go in release order? Do you wanna check out which game a character you like the design of came from? Do you think a specific game's gimmick seems fun? Do you want to check out PC-98? (Please. Please. Please. Please. Please.)

There is the elephant in the room though, which is that Touhou is more defined by fanwork than it is the actual games themselves. The issue is that it is REALLY hard to recommend a "start here!" and line when it comes to that wide web. I'd say check out some IOSYS MVs cause that's what got me and a lot of other people interested in the franchise, but you can also just go straight to drawings of Marisa and Reimu making out sloppy style if you want. There's also fangames but I haven't really checked out many so I don't feel too confident giving any recommendations.

If you end up not really liking the games but enjoying a lot of the fan stuff, don't worry cause that's like 99% of the fanbase LOL.