If you’re choosing a Python interpreter to use, I highly recommend you use Python 2.7.x, unless you have a strong reason not to.
Also use Python 2.7.x if you’re starting to work on a new Python module. If you have managed to get it working on 2.7, you can add support for older 2.x versions.
Python 2.x is the status quo, Python 3.x is the shiny new thing.
The difference between Python 3 and Python 2 is much greater, therefore writing code that works in both Python 2 and Python 3 is a very complicated process.
It is possible to write code that works on Python 2.6, 2.7 and 3.3. This ranges from tricky to extremely hard depending upon the kind of software you are writing; if you’re a beginner there are far more important things to worry about.
When people speak of Python they often mean not just the language but also the CPython implementation. Python is actually a specification for a language that can be implemented in many different ways.
CPython is the reference implementation of Python, written in C. It compiles Python code to intermediate bytecode which is then interpreted by a virtual machine. CPython provides the highest level of compatibility with Python packages and C extension modules.
If you are writing open-source Python code and want to reach the widest possible audience, targeting CPython is best. To use packages which rely on C extensions to function, CPython is your only implementation option.
All versions of the Python language are implemented in C because CPython is the reference implementation.
PyPy is a Python interpreter implemented in a restricted statically-typed subset of the Python language called RPython. The interpreter features a just-in-time compiler and supports multiple back-ends (C, CLI, JVM).
PyPy aims for maximum compatibility with the reference CPython implementation while improving performance.
If you are looking to increase performance of your Python code, it’s worth giving PyPy a try. On a suite of benchmarks, it’s currently over 5 times faster than CPython.
PyPy supports Python 2.7. PyPy3 , released in beta, targets Python 3.
Jython is a Python implementation that compiles Python code to Java bytecode which is then executed by the JVM (Java Virtual Machine). Additionally, it is able to import and use any Java class like a Python module.
If you need to interface with an existing Java codebase or have other reasons to need to write Python code for the JVM, Jython is the best choice.
Jython currently supports up to Python 2.5. 
IronPython is an implementation of Python for the .NET framework. It can use both Python and .NET framework libraries, and can also expose Python code to other languages in the .NET framework.
Python Tools for Visual Studio integrates IronPython directly into the Visual Studio development environment, making it an ideal choice for Windows developers.
IronPython supports Python 2.7.