I have been a Deadhead longer than a guitar player- but from my listening and reading about his style... you are on the right track with you banjo assumption. Garcia's early influences were bluegrass and old-timey music. In fact, one of the first versions of the what later became known as "Grateful Dead" was "Mother McCree's Uptown Jugband Champions." Garcia played banjo in Mother McCree's.

As Garcia and the Dead evolved and experimented with pschedelics, there playing became very free-form taking there influence from such Bay Area jazz innovators like Ornette Coleman. Garcia's use of modes and arpeggiation is more or less his "voice" as guitarist. In much of his solos, he incorporates the melody of the tune and embellishes around them. From my reading, in Garcia's early days he would sit around for hours and hours just practicing scales and modes- Myxolidian, Aolian, Lydian, etc.

Garcia can probably be identified as THE most unique rock guitarist EVER. I say this because he is not really a rock guitarist. He had so many influences outside of rock music that shaped his playing including bluegrass, jazz, country, old-timey, jug band, etc. Another amazing thing about Garcia's playing is that he tried to phrase his playing as a trumpet would be played. This was of course before the days of MIDI- listen to his playing and you will hear it yourself.

While this info is not very technical- it gives you an idea of where his playing was coming from.