I always hear so much about it around my parts of the net. But I've never played one myself, and they seem like so much fun. Especially the fighting ones! Even though I know next to nothing about them..
However, I run Linux. I stopped using Windows a few years back. Is there any way to play any of the Touhou games in Linux that does not mess up the game?

Also, which one should I start with?

With the release of Wine 1.0.1, most of the Touhou games run nearly flawlessly in Linux! Just install Wine 1.0.1 or later from your distribution's package manager and run your TH games.¹

The Article on the Touhou Project Wiki also contains instructions, tips and tricks to get the games to run as smooth as possible.
Additionally there is the official WineHQ AppDB, which lists lots of applications and games and their Wine compability. Quite a few Touhou titles have a Platinum-rating, meaning they should work perfectly fine!²

1 http://touhou.wikia.com/wiki/Running_in_Linux
2 http://appdb.winehq.org

I love how the stamp for this thread seems to refer to Call of Duty.

>>3
i assume it means "cash on delivery", due to the postal theme

Perfect cherry blossom or embodiment of scarlet devil are usually the recommended starter games!

>>5

Which one is cooler? :3

PCB is cooler. EOSD, on windows at least, is a little weird without the v-sync patch because of the input lag. It's also the only windows game without visible hitbox, which I think is really annoying, but probably doesn't matter so much if it's your first game. I think starting with PCB is a good idea, as it's fairly easy to clear on all the difficulties because of the border system and the huge amount of resources you get. Th 12 is my favorite, but I don't think it's a good game to start with because of the weird gimmick and difficulty.

Late but on the contrary, without thinking much about scoring, I would recommend Touhou 8: Imperishable Night, as recommended starting game. It's fairly easier compared to its two previous games, and you can play it with more ease despite having more confusing mechanics. Keep in mind that as the series goes on, the feel of each game gets different. Touhou 10 onwards has a different feel compared to its previous games, and so on.