Depends on what part of Touhou you're referring to.
Modern: Solar Sect of Mystic Wisdom ~ Nuclear Fusion [SA], A Star of Hope Arises in the Blue Sky (HSiFS), The Gensokyo the Gods Loved (MoF), Old Yuanxian (TD), Eternal Spring Dream (LoLK), Emotional Skyscraper ~ Cosmic Mind (UFO), UFO Romance in the Sky (UFO), and Lullaby of a Deserted Hell (SA).
Old: Shanghai Teahouse ~ Chinese Tea (EoSD), Gensokyo Millenium ~ History of the Moon (IN), Eternal Night Vignette (IN), Phantom Ensemble ~ Ghostly Band (PCB), Mystic Oriental Temple (PCB), U.N. Owen Was Her? (EoSD), and Wind God Girl (PoFV).
Older: Bad Apple!! (LLS), Complete Darkness (SoEW), Eternal Shrine Maiden (HRtP), and Faint Dream ~ Inanimate Dream (LLS).
Or for fighting games: Our Hisoutensoku (UNL), Bamboo Forest in Flames (ULiL), Catastrophe in Bhava-agra (Arrange Ver.) (SWR), Akutagawa Ryuunosuke's Kappa ~ Candid Friend (ULiL), and A Huge Shadow and a Tiny Conclusion (UNL).
The problem with fighting games being that they're mostly done by a different artist from ZUN. Also two of those don't play in the games.
I would rather get people into the modern era, as that's what ZUN makes nowadays. Of course, his style and music choices change whenever, so there's no perfect example of a Touhou song that fully represents his style.