Elvis Costello's favorite album of his own.

For me, it's "My Aim Is True".  Listen quite often to it.

Most people don't know that members of his backing band for his first album (band name Clover) became "the News" for Huey Lewis. Or, at least some people don't know that...

Right you are @jji666, which played a role in my liking it as much as I did. Plus Elvis’ vibrato wasn’t as over-the-top as it later became. I’m not generally a fan of what to me constitutes excessive vibrato, though there are exceptions (Iris DeMent and Maria Muldaur).

Clover, a SF Bay Area band, were over in the the UK in the mid-70's, a part of the burgeoning Pub Rock scene. Also a major player in that genre were The Brinsley Schwarz Band, whose bassist/songwriter/singer was Nick Lowe, who produced My Aim Is True. Nick later joined forces with Dave Edmunds in what became my favorite UK band of them all, Rockpile. Huey Lewis plays harp on a coupla solo albums of Dave's. 

i'd say "this year's model" is his best, in the sense that it rocks the hardest, (arguably) sounds the best and has no skippable tracks. the one i listen to the most, however, is the odds-and-sods collection, "taking liberties," which is the least contrived and freest-flowing.

Before any English teacher corrects me, I'll do it myself: The Brinsley Schwarz Band WAS a major player, not were. 😉 I was running short on time (for a scheduled doctor's appointment) as I was typing that sentence, and didn't proof what I wrote.