I strongly suggest that you install a complete scientific python distribution such as Anaconda or Enthought Python which contains all the packages you need for science (numpy, scipy, matplotlib, numba, pandas, etc.)
For scientific computing, the de-facto standard is to use IPython instead of python. It is a improved python interpreter, with batteries includes (indentation, completion, history, HPC, etc.).
For you IDE, Matlab-like, you have basically one choice: Spyder (which as a basic git support). The other IDE are nicers but they lack the tools for inspecting datasets. Spyder directly runs an IPython session which can be edited later on with other tools.
Another one IPython notebook (now known as Jupyter) which is a new and very powerful tool especially if you want to document your code with Latex code. Your IPython session is embedded and directly transferable to others, easily versionable.
You can also run an interactive presentation directly within the notebook, which is a nice way to show results. Think of it as the future of research, where your results are interactive. Anyone who can download the notebook will run the same exact experiments.
Take a look at the multiple examples already out there:
IPython notebook example
If you don't like to work in the browser, I suggest my setup which is:
Anaconda (python distribution with science packages)
Sublime Text 3 (lightweight code editor) with the SublimeREPL, SublimeIPythonNotebook
IPython Qt console (inline plotting, completion, saved sessions, saved datasets, etc.)
Remember that all the IPython front ends (IPython console, IPython QtConsole, IPython Notebook, SublimeREPL, etc.) can be connected to the same IPython core instance.
So, you can easily mix different tools at the same time depending on your needs (writing documentation, writing scientific stuff, code, presentation).
One IPython core to rule them all :-)
