The current production versions are Python 2.7 and Python 3.1.2.
Start with one of these versions for learning Python or if you want the most stability; they're both considered stable production releases.
If you don't know which version to use, start with Python 2.7; more existing third party software is compatible with Python 2 than Python 3 right now.
For the MD5 checksums and OpenPGP signatures, look at the detailed Python 2.7 page:
* Python 2.7 Windows installer (Windows binary -- does not include source)
* Python 2.7 Windows X86-64 installer (Windows AMD64 / Intel 64 / X86-64 binary [1] -- does not include source)
* Python 2.7 32-bit Mac OS X Installer Disk Image (for Mac OS X 10.3 through 10.6)
* Python 2.7 PPC/i386/x86-64 Max OS X Installer Disk Image (for Mac OS X 10.5 or later)
* Python 2.7 compressed source tarball (for Linux, Unix or OS X)
* Python 2.7 bzipped source tarball (for Linux, Unix or OS X, more compressed)
Also look at the detailed Python 3.1.2 page:
* Python 3.1.2 Windows x86 MSI Installer (Windows binary -- does not include source)
* Python 3.1.2 Windows X86-64 MSI Installer (Windows AMD64 / Intel 64 / X86-64 binary [1] -- does not include source)
* Python 3.1.2 Mac OS X Installer Disk Image (for Mac OS X 10.3 through 10.6)
* Python 3.1.2 compressed source tarball (for Linux, Unix or OS X)
* Python 3.1.2 bzipped source tarball (for Linux, Unix or OS X, more compressed)