It seems that there are more than a few Elvis Costello fans here on this forum which is really great and therefore this thread should hopefully make for some interesting reading.
Here are a few of my favorite Costello recordings, listed in order of their original release date.
"This Year's Model" (1978) - the early, angry Elvis at his acerbic best.
"King Of America" (1986) - Costello's first post "Attractions" release finds his song writing reaching newer and higher peaks. Playing like a song cycle, the last few songs on the first side and the entire second side of the original US LP release is classic from start to finish. "Suit of Lights" and "Sleep of the Just" are two of Elvis' greatest songs.
"All This Useless Beauty" (1996) - the Attractions' swan song is perhaps also their greatest work. Costello's song writing is fully matured and brilliant in very way imaginable. The title song and "Poor Fractured Atlas" are Costello at his best. This recording is far too often and undeservedly underrated.
Those are my top three. There are many other very good Costello recordings but for me these three stand out from all the rest.