Andy Field's Discovering Statistics Using SPSS is great, and a very, very easy read.
I don't know how your program runs, but our stats sequence is two classes... the first is basics, probability theory through one-way ANOVA. The second is univariate ANOVA/ANCOVA of different flavors, correlations, and linear regression of different levels of complexity. If yours is similar, you might not even be using SPSS for the first couple of months. Hell, you might be doing things by hand (or using Excel, which is almost like doing it by hand). Don't stress too much over it now.
Chances are you won't get to the fun, complicated stuff (factor analysis, MANOVA/MANCOVA, logistic regression, ect.) unless you take a specific class on it.
By all means, get a book, do some reading this summer... but don't think you have to memorize the thing before August. It won't be that bad 😀