You should download the
Windows X86-64 MSI Installer (2.7.7) because your system is 64-bit. x64 uses a link register rather than pushing return addresses on the stack, so its a tad bit safer than its x86 counterparts. In addition, the x64 code will likely run a little faster.
For completeness, you could run both x86 and x64 on a 64-bit Windows machine. But the reverse does not hold true.
You might be able to install Python 3.4, too. But you have to be careful because Python broke some prominent features between 2.x and 3.x. If you get mysterious errors when using Python 3.x, you should try using Python 2.x (or run Python's 2to3 conversion program on the 2.x Google is very specific about the Python versions, and 3.x is not allowed. Its likely due to the Python 3 redesign and improvements that were not backwards-compatible.
*.py source files).