As a music geek, I somewhat regret not getting the Pixies sooner. My first pass at deepening my music knowledge beyond "What's on the radio right now" was in 2000-2001, when I would click around Allmusic to find out what bands influenced bands I liked. Somehow, Pixies kept coming up, and the song that was put before me was "Where Is My Mind." That's a great song, but for my little 14-year-old brain, it was just a bit much. A bit too off-kilter.
I went back to them about three years ago after a snippet of "Gouge Away" was used in an episode of LOST. When I heard it I needed to go back and pull them out of the file. The way Black Francis goes from menacing muttering to psychopathic screaming really worked for me and showed exactly why they're considered an influence on Nirvana. It's simple, you just need to do it well. This, I think, is the song you would ideally start with if you want to show somebody "This is what the Pixies are." Then you're open to all this other wonderful stuff, including "Where Is My Mind."
Probably my favourite song by them is "Here Comes Your Man." It's incongruously sweet and poppy, almost a sarcastic take on a radio single, because although there are chiming, peppy guitars, there's a dreary undertone that you can't quite put your finger on why or how... until you do a bit of research and find out the song is about homeless people dying in an earthquake. It's the spiritual ancestor of "Pumped Up Kicks" in that way, and it's a bit sad that people, including the bandmembers themselves, think of the song as an unrepresentative bit of mainstream kitsch. I think it suits them well.