I've skimmed briefly "Principles and practice using C++", "Accelerated C++" and "Thinking in C++".
The initial impressions:
"Principles and practice" feels monolithic to me: About 1200 pages length and very in depth. Nevertheless, it feels like a good reference.
"Accelerated C++" it's a bit clunky. Best suited to people with experience in various programming languages.
"Thinking in C++" is a pretty good introduction to programming, OOP, and C++. The writing style is clear and both volumes are freely available. I would go with this one.
My thoughts are, we first need to know the level of knowledge each group member have, and then try to reach a consensus for using the same learning material, as we could organize the assignments best. Feel free to comment either here or in the Google groups page.