are the things I'm practicing right now, to answer your question. After years of playing on both nylon and steel strings, about two years ago I abandoned the guitar pick and steel strings completely and have gone to just fingerstyle guitar on nylon. I go through a daily ritual of practicing a list of tunes at least once, such as:
All The Things You Are
Skylark
Body And Soul
Here's That Rainy Day
Moonlight In Vermont
Blue Bossa
Wave
Willow Weep For Me
On Green Dolphin Street
How Insensitive
Quiet Nights Of Quiet Stars
...and about two dozen others. I mainly play the jazz heads with chord-melody combined but I try to stretch out on a few tunes with solos interspersed with chords. I also play a few classical pieces. I mix in some pop tunes as well, such as ones arranged by classical guitarist Mario Abril in his arrangement books (La Paloma, Theme From Love Story, Alfie, etc.). If you are interested in going this route there is an extraordinary series of books by jazz guitar great Robert Conti (
http://www.robertconti.com/) that gives you the entire chord-melody arrangement for many jazz standards. I've used several of his sophisticated chromatic arrangements for my repertoire. They are head and shoulders above any other jazz standard books for guitar I have seen.
Regarding "Trane", I assume the person was speaking of John Coltrane, the late great tenor and soprano sax player who is truly one of the jazz giants of all time. His tunes are required study for anyone contemplating a career in jazz. "Giant Steps", with its quick and frequent key changes has been a sort of rite of passage tune for jazz guitarists to master (or any other instrumentalists for that matter).