Starting with Touhou 6, the games are released on the PC. So, if you have a computer compatible with Touhou 6, then I believe all the games from Touhou 6 to Touhou 16 are accessible.
Important to note...you DON'T have to play the games in a specific order. Each game has a different plot. However, what the plots of these games have in common is that they are "incidents" caused by the final boss.
Erm, I actually have a little lore from the games, so if you wish to actually follow how the incidents connect with one another, I recommend that you play Touhou 10 before Touhou 11. And maybe Touhou 12 before Touhou 13.