Komodo Edit meets most of your requirements (as others mentioned in the comments) and supports Python 3 from version 6:
- Open source and free.
- Cross platform (Windows and Linux, also Mac) ― built on XULRunner.
- Standard features: syntax highlighting, auto-indent, etc. ― Komodo has the best Python auto-completion I've seen; they'll do automatic type inference from variable assignments.
- Run button, rather than console where you have to type "python foo.py". ― Can be simply added.
- Context-aware help ― supported when you press ( plus it will do this nicely on objects that have been instantiated from other classes.
- Embedded Python shell ― The full Python shell integration is only in the commercial IDE, but you can easily hook up a shell into a command output window by adding a toolbox recipe for
python -i.
- Built-in debugger ― Unfortunately not (but neither do lots of the light-weight IDEs recommended above) ― this is only in the commercial Komodo IDE. I'd recommend using Winpdb alongside Komodo Edit for development ― it's faster than the Komodo IDE debugger (and lots of other debuggers) in my experience. Whether this'll fly with high school students would be the question.
- Useless crud stripped ― Komodo's clearly got more stuff in it that IDLE so it depends how you see this. Auto-completion can be turned off.
- Lightweight for kids who go home to old PCs unable to run beefy IDEs such as Eclipse ― This may also be a downfall ― I'd say Komodo is less beefy than Eclipse though.
Extra things to consider:
- Komodo is great at web development: it supports nice syntax highlighting and code completion on embedded CSS inside HTML etc…
- Support for extensions (along the same lines as Firefox, plus the extensions can be written in Python) ― this could be useful if you need some tweaks to the UI etc for the courses.
