I'd suggest that you should learn Python3. Although there still is much Python2 code around, Python3 is the future, so if you're going to spend time learning one, why not learn the one with the longest future?

Here's some useful links:

This is the official "Python 2 or 3?" page from the Python developers.
https://wiki.python.org/moin/Python2orPython3

This is a free online resource for learning Python3:
http://www.learnpython.org

The Python site has many links to tutorials for beginners and more experienced programmers.
https://wiki.python.org/moin/BeginnersGuide

This is a great online free book, Dive Into Python
http://www.diveintopython3.net

Hope that helps
Rachel