List of recommended  concertos: 

 

Violin:  

 

Pyotr Ilyich Tchaikovsky: Violin Concerto in D major, Op. 35
Ludwig van Beethoven: Violin Concerto in D major, Op. 61
Johannes Brahms: Violin Concerto in D major, Op. 77
Jean Sibelius: Violin Concerto in D minor, Op. 47
Felix Mendelssohn: Violin Concerto in E minor, Op. 64
Max Bruch: Violin Concerto No. 1 in G minor, Op. 26
Édouard Lalo: Symphonie espagnole in D minor, Op. 21
Antonín Dvořák: Violin Concerto in A minor, Op. 53 (B.108)
Béla Bartók: Violin Concerto No. 2, BB 117
Henryk Wieniawski: Violin Concerto No. 1 in F sharp minor, Op. 14

Wolfgang Amadeus Mozart: Violin Concerto No. 3 in G major, K. 216
Wolfgang Amadeus Mozart: Violin Concerto No. 5 in A major, K. 219
Wolfgang Amadeus Mozart: Violin Concerto No. 4 in D major, K. 218
Johann Sebastian Bach: Violin Concerto A minor
Johann Sebastian Bach: Violin Concerto E major

Niccolo Paganini : Violin Concerto No.1 in D major, Op. 6

Alexander Glazunov: Violin  Concerto Op. 82

Edward Elgar: Violin Concerto Op. 61

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Piano:

 

Johann Sebastian Bach: Concerto No. 1 in D minor, BWV 1052

Johann Sebastian Bach: Concerto No. 5 in F minor, BWV 1056

Joseph Haydn: Keyboard Concerto in D major, Hob.XVIII:11

Wolfgang Amadeus Mozart: Piano Concerto No. 20 in D minor, K. 466

Wolfgang Amadeus Mozart: Piano Concerto No. 25 in C major, K. 503

Ludwig van Beethoven:  Piano Concerto No. 1 in C major, Op. 15

Ludwig van Beethoven: Piano Concerto No. 3 in C minor, Op. 37

Ludwig van Beethoven: Piano Concerto No. 2 in B-flat major, Op. 19

Robert Schumann: Piano Concerto in A minor, Op. 54

Camille Saint-Saëns: Piano Concerto No. 2 in G minor, Op. 22

Frédéric Chopin: Piano Concerto No. 1 in E minor, Op. 11

Frédéric Chopin: Piano Concerto No. 2 in F minor, Op. 21

Felix Mendelssohn: Piano Concerto No. 2 in D minor, Op. 40

Felix Mendelssohn: Piano Concerto No. 1 in G minor, Op. 25

Maurice Ravel: Piano Concerto in G major

Sergei Rachmaninoff: Piano Concerto No. 2 in C minor, Op. 18

Sergei Rachmaninoff: Piano Concerto No. 3 in D minor, Op. 30

Sergei Prokofiev: Piano Concerto No. 1 in D-flat major, Op. 10

Sergei Prokofiev: Piano Concerto No. 2 in G minor, Op. 16

Sergei Prokofiev: Piano Concerto No. 3 in C major, Op. 26

Pyotr Ilyich Tchaikovsky: Piano Concerto No. 1 in B-flat minor, Op. 23

Edvard Grieg: Piano Concerto in A minor, Op. 16

Dmitri Shostakovich: Concerto in C minor for Piano, Trumpet, and String Orchestra, Op. 35

Dmitri Shostakovich: Piano Concerto No. 2 in F major, Op. 102

Béla Bartók: Piano Concerto No. 2 in G major, Sz. 95, BB 101