Learn a WHOLE CONCERTO! Do not just do a few movements-whoever said that is got to be kidding. Musicians do not leave unfinished repertoire! Also, Saint Saens no. 2 is DEFINITELY NOT a starting concerto! It is a very difficult piece, both technically and musically, particularly the first movement.
Based on your repertoire, I would stay away from the Romantic concerti-Liszt, Tchaikovsky, Rachmaninoff are not for beginners. Even Mozart's K466, K467, K488, and K491 are difficult. Additionally, Rachmaninoff is not the hardest-Mozart is. Anyone can play Rachmaninoff.....as long as they have sufficient technique. I hear Rachmaninoff and Tchaikovsky played all the time in competitions. But I never hear Mozart, because either people are deceived by its "simplicity" or find Mozart too difficult.
Some good beginning concerti include:
Haydn D Major Concerto
Beethoven 1
Kabalevsky 3
Shostakovich 2
The four I just listed are some of the most popular starting concerti-they are very straightforward musically. Beethoven 2 is not easy-I must warn you, because, like Mozart, the simplicity deceives people into thinking it is easy, but it is not. Beethoven 1 is a popular concerto played by youngesters, and is not as hard as no. 2. The Haydn D Major, Kabalevsky 3, and Shostakovich 2 are good options too.