I'm going to go out on a limb and say that this is the single best movie in the entire Marvel Cinematic Universe.
The exploration of friendships and trust was stunningly well done. Friendships betrayed over ideals, history forgotten in new circumstances, and the risk you inherently take in opening your heart to someone—and not a hint of romance to cloud the issue! Combined with brilliant performances, adrenaline-packed action sequences, and world-changing scope, this is just the best MCU movie to date.
Of course, it doesn't exist in a vacuum, so be sure to watch the first Captain America and the almost-as-good Avengers for background. Which might lead you to the other movies, the TV series, or even the original comics!