Another thing to note about the statistical packages is what bignose stated: bottom line, if you do not know what a test is doing (ie. test of location - mean or median, variance, etc) you probably won't know the assumptions required for the test to be run in the first place. That being said - if you do, most programs will give you the proper information in the output as long as you know what to look for.
Example: If you run an ANOVA test (equal variance assumption - others should be worked out in the study design) SPSS will use a Levene statistic to test before it gives you the results from the ANOVA - if Levene fails, than obviously the ANOVA is irrelevant, and you have unequal variances (Try a Welches ANOVA in this case). I believe SAS uses a Folded-F test to do the same thing.
In my opinion the understanding a statistical package is a great compliment to the skill, and it looks good on a resume. I would have to recommend SPSS as it is becoming more common, and easier to use than most packages. It also has an interface similar to an excel spreadsheet.