There is a suitable software for Statistical analysis. I am aware of the models and variables and try looking for the best software for their calculations.
They're all going to allow you to do basic things such as chi-squared tests, Fisher's exact test or logistic regression. I'm a heavy R user but I thought JMP was very beginner-friendly.
They should all give you the same result. If they do not then you have some other problems. I have extensively used R, STATA, and SAS. Which one I use usually depends on: 1) access to the software 2) If the routine exists or I have to write the routine myself 3) ease of use. Meaning, what additional steps do I have to do to read in the data. If it is already in STATA format, I go with STATA. Is there a lot of missing data? I might go with SAS as I am more familiar wight he missing data routines of SAS. What is important to you for ease of use may be different from me, so use what you know.
I would recommend SPSS from my long using experience, but in SigmaPlot you can arrange and analyze data more easily than any other softwares, along with this, SigmaPlot can give you more specifically desired graphs rather than SPSS and R. If you need excellent statistical graphs, there is the only option: GraphPad Prism.
SAS is now free for Universities (SAS University Edition, see http://www.sas.com/en_us/software/university-edition.html), and there are many new techniques available for discrete data (Stokes & Koch, Up To Speed With Categorical Data Analysis, Paper 346-2011 SCSUG 2011)..