Wolfram Mathematica, MATLAB or something else? I have only a little experience in math calculation tools. So please don't be strict if my question is not well defined :)
Which tool (Wolfram Mathematica, MATLAB or something else) is better to use for statistics? Where can I find quickstart guides and tutorials for it?
 A: For statistics I would recommend R - computation environment concerning statistics. 
Here you can find many tutorials for R.
A: There are specific tools out there for statistical analysis. For example, R, SPSS, and Minitab.
Nevertheless, both Mathematica and MATLAB are capable of doing the required computations; which is "better" is a matter of taste and application requirements, most of the time.
MATLAB doesn't ship default with many statistical subroutines. However, it does have a Statistics toolbox that contains much of the functionality found default in some other packages. It all depends on what exactly you're trying to do, statistics wise, and what your comfort level with programming is. Maybe you can elaborate more on what you're attempting.
(Of course, the man-hours spent re-programming an algorithm for, say, ANOVA is often costlier than just buying the license to the toolbox that has a stock routine outright).
Finally, to answer your question, I personally prefer MATLAB. I find that it is easier to program in and allows for easier rapid development and testing of algorithms, etc. Syntactically, I prefer MATLAB. MATLAB likes to keep things close to pseudo-code. Mathematica tries to keep things closer to mathematical notation.
You can find MATLAB tutorials all over the internet. Just google "MATLAB tutorial" and you'll have a slew of results.
A: Wolfram Mathematica is a very capable software for doing statistics, and unlike Matlab, its statistical functionality is included in the core Mathematica. 


*

*Unlike R or Matlab it provides symbolic support for probability computations. You can peruse Probability & Statistics guide page to get an idea about the functionality.

*Mathematica is often faster than R for statistical data crunching. 

*Mathematica has superior statistical visualization functionality. See Statistical Visualization guide page on the web.

A: Some people would say that Matlab is for numerical matrix calculations and simulations, and Mathematica for symbolic calculation.  But nowadays both can perform both things. And we should add another contender, Maple.
In my opinion Matlab is too big and needs too much resources. You should only choose it if your company or school forces you or if you need some rare simulation tool.
If not, you should choose Mathematica or Maple.  They are also very good with graphics, numeric matrixes and both have simulation tools.  But they have something much better than Matlab: symbolic and abstract mathematics.
If you can't afford commercial software or you like free software you can try R, for statistics and little bit more.
