The lachrimae Pavan was composed by John Dowland in the 17 century. This piece is very popular, there are hundreds of manuscripts and arrangements over this song and it has served as inspiration for many composers.
Frederic Chopin (1810-1849) was one of the greatest pianists/composers of the 19th Century. He has never written for guitar but I have found good arrangements of some of these Preludes for the solo guitar by Fransisco Tarrega.
A series of arpeggios that could be used as a rhythm part, but can be played as a stand alone tune. It's an exercise which can be played either by fingerpicking or with a pick.