I would also recommend the other Mozart Masses - the C Minor Mass and the Coronation Mass. After that, though, to keep it within the classical period, I would also recommend some works by Haydn. Particularly, look at his Missa in Angustiis, also know as the "Nelson" Mass. Very nice, majestic work. From there I would turn to, what I consider, one of the best masses out there - Bach's incredible Mass in B Minor. It is incredible. Beethoven's Missa Solemnis, to me, ranks right up there with Bach's mass, although it was written around the time he was composing his 9th symphony, so it begins to sound a little more Romantic than Classical, but not that much of a jump. For straight-up requiem, though, my top recommendation is Brahms' "Ein Deutsches Requiem." Not a proper requiem in the strictest definition, but it is incredible.
Luckily the genre of religious choral music is incredibly rich, containing some of the most beautiful works created. If you really want to go hardcore, try some Renaissance a cappella masses and requiems - composers like Ockeghem, Palestrina, des Prez, Tallis, etc.