The 5 piano concertos are among Beethoven’s most played and recorded compositions. Searching for a complete series I listened to Pollini, Gould, Schiff, Arrau and Barenboim. Arrau and Barenboim deliver the best of all 5 concertos, with Gould being irrelevant, Schiff and Pollini superficial (especially Abbado’s conducting). Of course, the Barenboim-Klemperer recording is considered classical, but Arrau with Davis is one you can’t ignore. There exist also individual recordings of specific concertos which have a special value, as is the Argerich-Abbado recording of the 3rd concerto (they play also the 2nd, but not that well).
Only recently I listened also to a recording of the complete concertos with Aimard and Harnoncourt. Harnoncourt is a little ‘cold’, offering performances to be studied rather than to be enjoyed. His collaboration with Aimard in Beethoven’s concertos resulted to an interesting recording, that makes some difference, especially when it comes to the distinction of the various voices in the orchestra along with the piano. He is also not too fast, which came as an additional and pleasant surprise. I would keep this recording along with Barenboim and Arrau.