Recommendation for best Joe Jackson records?

It depends on your music tastes. Each album has a certain flavor of music that Joe seems to flesh out with ease. To really get to know him and his music, I would start at the beginning with "Look Sharp!" and just keep on going through the years (Discography). IMO there are no "dogs" (some are an aquired taste!).
If I had to pick a favorite, it would be "Beat Crazy" .

Thanks everyone, I just ordered five of his LPs from my trusted vinyl-dealer in Germany, according to your recommendations.

"Beat Crazy" is my favorite but his music is varied in styles. From swinging jazz to Movie soundtracks he's done it all. If you live near a record store that has used vinyl you will find alot of his stuff cheap and if your patient alot of it will be in mint shape. Look around for a used copy of MOFI "Night and Day",it is one of there and his better offerings. In his early years he had to bear the cross of being compared to Elvis Costello and rightfully so their music sounded very similar for the two albums. Look at the cover to "Body and Soul",he was trying to replicate the look of the original Blue Note album covers of the late 50's to late sixties.

Look Sharp, Night & Day, and Big World are all essential JJ recordings.

Night & Day and Body & Soul are two of my favorites. If you enjoy big band music also check out Jump'n'Jive. He also wrote an autobiography outlining his life & career - can't recall the name - it was slow reading for me.