You can download trial versions of each game on
ZUN's website. You can also download the trial version of TH16 on
Steam.
Some common starting points are Touhou 6 (EoSD), 7 (PCB), 8 (IN), 14 (DDC) and 16 (HSiFS), but really just pick what seems the most inviting. EoSD is effectively the "first" game. The games have self-contained stories and can be played without concern for an overarching plot, but the series does have a rather extensive chronology and many characters from earlier entries make appearances as playables and whatnot.