There are some free software pacakges recommended to group members: LaTeX for wordprocessing (convenient if you have math in your document) and the Python programming language with Numpy / Scipy and matplotlib for numerics and plotting.
They are easier to install on linux and (I think) mac systems than on Windows. These versions work well on Windows:
LaTeX for Windows
I recommend the WinEdt editor and MikTeX distribution. The former is designed to work with the latter.
WinEdt page (free for 30 days, then $29, worth it)
MikTeX page (free / Gnu license)
Python for WindowsThe pythonXY distribution comes bundled with some nice editors and almost all the packages you would need -- saves a lot of trouble.
If you go this route, be sure to update the NumPy and SciPy binaries from this site; they link to the Intel MKL and are about 10x faster on my systems.