How do I learn jazz standards?

Hi everybody,

I'm a mostly self-taught musician who mainly plays acoustic guitar. I've recently been learning certain versions of jazz standards for fun, girl from ipanema, autumn leaves, and I've been trying to pick up a few others, but I feel like I'm hitting a brick wall. I'm having trouble upgrading from mimicry to a more holistic understanding of the pieces. For example, if I were to play with someone else in another key, I'd have to fumble around a bit to transpose it mentally. I guess that may be caused by me learning only specific versions. Some questions:

• Does anyone have tips for learning standards?
• How can I locate the "purest" form of a standard, if that even makes sense? I feel like learning certain interpretations with their own flair isn't ideal.