Hitch

Well, here are select pieces by well known composers which I think is very ideally suited for beginners. I just went by the composers that popped into my head immediately. All of these are very melodious, but long and complex enough to appreciate nuances.

Schubert's Trout Quintet - Movement 4

Schubert Trout Quintet - Thema con Variazioni - Andantino - Allegretto - YouTube

Haydn's notorious String Quartet Op. 76 ('Emperor'), which is also the theme for the German Anthem. Very simple, but the melody will melt your ears.

Joseph Haydn String Quartet op 76/3 'emperor' in C-major (mov 2/4) Poco Adagio cantabile - YouTube

Beethoven's 7th Symphony - Movement 2

Beethoven, Symphony 7, Allegretto, mvt 2 - YouTube

Leoš Janáček's Sinfonietta

Leoš Janáček - Sinfonietta

Ralph Vaughan William's Fantasia on a Theme by Thomas Tallis

Fantasia on a Theme by Thomas Tallis - Ralph Vaughan Williams - YouTube

Bach's Well-Tempered Clavier (this is only the Prelude and Fugue of Book I)

Prelude and Fugue No. 1 in C major, BWV 846, from Bach's Well-tempered Clavier, Gulda pianist - YouTube

Edit: Also, although Youtube does have a very good selection, its upload quality is terribly suited for Classical music. So, listen but try to get your hands on FLAC downloads or buy them off Amazon or preferred site.