I've recently committed to learning to sing and sing while playing. What I've figured out is that for learning songs, what works well for my style and for my method of learning is playing songs that are played with only bass accompaniment, or with mainly bass accompaniment. A great example of what I mean would be Kurt Elling's rendition of "Lonely Avenue", which is arranged in only vocals, bass, backup vox, and finger-snapping for percussion. It's relatively simple to adapt to a solo form, and would give me something "complete" to practice, rather than just playing over a bassline which sounds empty without the upper harmony or drum percussion. I know that some songs can be adapted well to solo bass, but I don't want to go through that work just yet. I just want to learn to sing. The meat of my question, then, is if anyone else knows other songs which sound "complete" with just vocals, bass, and basic percussion (feet, tambourine-stomping, etc.) Jazz, soul, or blues are preferable, as I play those genres often, but I'm open to expansion. (I'm not exactly sure what forum this belongs in, as it's not a request for tabs or strictly a technique discussion... sorry if I have misplaced it.)
...I really should've thought of that one, considering I've learned both of them for the same upcoming gig.
I used to do "Over The Rainbow" pretty often at open mikes. I found a bunch of different charts to facilitate varying harmonization and then learned the head on bass so I could do unison lines or even reverse roles and sing harmony under bass playing the melody.
Early Police and Early Beatles got me started and when you get really advanced you can try and tackle Geddy.
I can sing harmony parts while playing bass, but singing lead takes a LOT of concentration. T. Michael Coleman used to do a funny bass song just to make the point... can't find it though.
Money by Pink Floyd is a great tune to practice playing and singing. There's that long instrumental section in the middle, but the the bass carries the song on the verses.