“I like greatest-hits albums,” Britt Daniel says. “The first record I ever heard by the Cure was Standing on a Beach. The first record I ever had by New Order was Substance. That’s the way I found those bands, and then I went backwards.”

Spoon, the lean, wily rock band that Daniel has led since 1993, are not the most obvious choice for a compilation of that kind. They have all the hallmarks of an albums act, known more for their consistently excellent long-players than for any hit singles as such. (Quick, name the best Spoon album. Bet you said Kill the Moonlight or Ga Ga Ga Ga Ga — unless you’re truly wild, in which case you picked Transference. Now think of their biggest song. Harder, right?)

This year, though, with a summer tour opening for Beck and Cage the Elephant approaching, Daniel challenged himself to put together a beginner’s guide to Spoon. The result was Everything Hits at Once: The Best of Spoon, the compilation they released in July. “It’s not really a completist’s greatest hits,” explains the singer-guitarist, 48. “It’s more like the cream of the crop.”

For this feature, Daniel chose a different set of 15 songs to tell the story of how Spoon went from unknown Texas noisemakers to major-label flame-outs to one of the most acclaimed rock acts of the last 20 years. “There are worse things to talk about,” he says, settling into a chair at his label’s downtown Manhattan office.