I've never met anyone who feels neutral about Beat Happening - you either love them or hate them, right? I remember when I used to play Beat Happening records in the store and most people had an immediate reaction. Unfortunately it was almost always a negative one. The primary complaint was Calvin's voice (followed by their seeming lack of skill at their instruments) and I do understand that it's not for everyone. Neither is free jazz or field recordings or grindcore, no? Whatever, to each their own. (I must say, following up Beat Happening with The Shaggs would have probably sent people over the edge but The Shaggs stuff hadn't been re-issued yet. Unfortunate.)
Anyway, the most charming thing to me about Beat Happening was the fact that it was amateurish. It was empowering to hear music that seemed within reach to make. The lyrics were always sweet even in the more sexual songs. I feel like Calvin pulled off the highly sexual sweet boy very well. Heather's songs were always winners and brought something extra special to the band. Her voice was more traditional so I always felt that her songs were a good way to dip a potential fans toes into the Beat Happening waters.
It was nearly impossible for me to pick just two songs. My favorites change all the time. (At one point back in the mid 90s I had made a Beat Happening mix and every song on it was my favorite. It was right after a break up and some days it could nearly send me to tears.) I feel like these songs are very good introductions to the band. If you can spring for the box set I highly recommend it.