Numerous resources will serve you during your lifetime of scholarship; this site spotlights some (though certainly not all) of the most helpful.
Free and Open-Source Software
For typesetting and document preparation, LaTeX is the best of the best. LaTeX is free typesetting software that renders professional-quality pdf files. An open-source software called LyX provides an intuitive graphical user interface that allows users to typeset in TeX by clicking instead of coding. For additional information and links, visit this site's LaTeX page.
For numerical computation and especially statistics, the open-source software R is widely used and often recommended. Users of R will have to learn a bit of the programming language, but the functionality and flexibility of R (not to mention the price -- free!) is well worth the effort. For less involved computations or for symbolic manipulation, the online computational engine Wolfram|Alpha provides a function and feel similar to those of Mathematica.