gridjam

FINALLY an answer JC.

to the the first half of your question- both and all.
I am into really learning analyzing the standards-lyrics, verses (if there is one) and then shedding them in various keys, meters,tempos,reharms,etc..
I'm finding that there are better keys (or more interesting keys) sometimes, that aren't the original or the taught keys that we are used to.

As of this writing I'm pretty well frustrated with the word jazz and many of the staunch systems of learning that seem to be affiliated with it, (whatever 'it' may be) so it's hard for me to offer any organized advice, aside from learn as much music as possible. Write and arrange too, transcribe and PLAY and talk about playing and the music with open-minded players!!!
It seems to me, in this- our info-saturated world, that we ought to be learning and ingesting forms of music from all over the place as well as finding things we love that are relevant to building a strong 'jazz-based' vocabulary. If we check out Africa, South America,and yes, the American classic song book,the Beatles, Bjork, Bartok, Bach, we can more easily adapt to whatever musical environment we find ourselves in.
(The arrangements I make over standards are often inspired by these reference inspirations and beyond)
With that in mind,there is something special about learning a standard (really knowing it) and doing with it what Miles and the boys did at the Plugged Nickel with If I were a bell, etc.. It gives one a strong thread to hang on to while venturing into all of the areas of music that may be made available and explorable based on who we are playing with.

When we play sessions at our place,we always begin with a tune or two before reading originals, or we just play free, coming up with grooves and tune-like material in response to one another.
Last thought-
I grew up hearing and knowing quite a few of the tunes (thanks to my Mom) that I found helpful in jam sessions,etc and am indebted to her for life for providing me with such a strong understanding and appreciation of songs and stories. Two things I am noticing that are lacking greatly in the younger players of today are story-line and meaningful melody content. There is no doubt in my mind that learning tunes in their bare-bones no extra frill fashion contributes greatly to my ability to play changes and still (hopefully) say something interesting as I develop my ideas throughout my 'soloing'. It also makes for fun times over the one chord vamps!
hope this helps to inspire. Not sure I'll ever feel qualified to teach anyone music, but I do aspire to set some fires and fan the flames as much as possible.
:)

IJ