You have to seperate tunes as being "standards", aka tunes from the great American songbook, from "jazz" tunes, which are anything from bebop to modal, etc. The standards are what you should work on in 12 keys, simply because singers do them in any key, and there are quite a few that don't have a "normal" key and will be played in all kinds of keys.
Get a song list, something like this: http://www.ryanjanus.com/PDFs/tune_list.pdf
and start going through the standards, i.e.
All of Me
All of You
All The Things
Unless of course you have all the time in the world and are a fast learner, in which case go ahead and take Dolphin Dance through all 12 keys; it would be great ear training.