Essential repertoire is going to depend a bit on what level player you are.
Someone who’s been playing a few years may be ready, for instance, to take on a piece like Saint-Saens’ The Swan from the Carinval of the Animals. It’s perfect for someone who’s up to shifting, just beginning to play in thumb position, and is great for getting a lovely tone with vibrato as well. More advanced players may want to learn the Brahms Sonata. Also the Beethoven Sonatas are fun, especially the first three.
Regarding Etudes, I’m fond of the Alwin Schroeder 170 Foundation Studies, a 3 volume collection of cello etudes from several pedagogues (Buchler, Dotzauer, Franchomme, Grutzmacher, Lee, Schroeder). And then the Popper High School of Cello Playing. In this case “High School” means college (Hochschuele) as opposed to secondary school (Oberschule).
There are many concerto “musts” – from the Goltermann, Boccherini and Vivaldi Double, the Haydn C and D Major concerti, theTchaikovsky Rococo Variations, Dvorak, Elgar, Brahms Double, and we haven’t even gotten up to 20th century staples.