Hi John,
You don't necessarily need a long song list, just improvise!!!
I have a friend who plays guitar and i get him to play chords which i then improvise over! A upbeat major key Blues improvisation goes down well, but we play lots of simple chord patterns two then i improvise a piece over the top, usually creating a short riff or A section to the piece then massive energetic solo!!!! then repeat the riff or A section that i played before, making the piece sound professional. Improvising always goes down well cause you play whatever you think sounds good whether its a loud mad ('jeff coffin' style) solo or some slow soulful playing (LeRoi moore style) (Both previous/current Dave Matthews Band saxophonists)
I find the improvised pieces great for busking because you can play in your own style, you can makE the piece as long or as short as you want! Plus it never sounds the same! I also find improvising so much more enjoyable and improves my playing dramatically.
However you would need a guitarist some sort of backing to make it work.
Other things that i found that worked are playing famous short jazz pieces then going into improvisation, such as Summertime, Watermelon man and Song of my Father, very simple pieces but the improvisations after the main melody really build up the piece and again you can carry on for as long as you want playing this, you can get lots of improvisation books like this which will come with a backing track to improvise over.
I've also played some Maceo Parker songs, funky sax can go down well and a great opportunity for solos.
Other Jams are good just picking a scale/key signature and playing whatever you feel like such as some jazzy solos.
Making use of the guitarist ive also played some Dave Matthew's Band stuff, playing extending sax solos such as the '#41 solo' (listener supported version) search for it in youtube from 5mins15 is the the sax solo from LeRoi.
Playing some popular songs from a Jazz Fake book with Backing chords has worked well too, but overall i find the massive improvisations over chord patterns and blues improvisation the best and the most fun too!!!