Yes, the Python Package Index (PyPI) seems to have become the Python repo of choice. But I seldom install packages directly from PyPI; almost every package that is reasonably mature has been packaged for Ubuntu, so I usually install from Ubuntu repos.
Running more than one version of Python on a machine SHOULD work. I have Python 2.7 and 3.something on my machine and no problems.
But I have heard from people whose experience has not been good. I don't know of anything like perlbrew to make it less painful. I would probably resort to virtual machines with one version per VM.
I run mostly Red Hat-like distros and use the yum tool as their equivalent of apt-get. When I need a python package that isn't in RPM format, there's easy_install.
I used to do my quick-and-dirty stuff in Perl, but CPAN has a bad habit of delivering broken modules. The python eggs have always seemed to run without problems. I credit a lot of this to the fact that unlike Perl, you don't have to compile a lot of C code to get a module going. So mostly I do only things that use basic Perl modules and are regex-related now. Anything else in the Q&D department I usually do in Python.
I don't normally attempt to switch Python versions on a single machine, but you might want to look at the "alternatives" facility. If Ubuntu has support for alternate versions, that's probably what controls it.
An IDE is no substitute for an Intelligent Developer.