Most test-selection mistakes happen before anyone opens SPSS. They happen when the variable type and study design were never clearly identified. Here's a short route from data to test.
Identify your variable types first
Is your outcome continuous, ordinal, or categorical? Is it normally distributed? These two questions eliminate most of the menu before you've compared a single group.
Match design to test
Comparing two independent groups on a continuous, normally distributed outcome points to an independent-samples t-test. The same comparison on a non-normal or ordinal outcome points to a Mann-Whitney U test. Paired measurements change the answer again.
Check assumptions before you trust the result
Normality, homogeneity of variance, and independence of observations are usually assumed and rarely checked. A quick assumption check takes minutes and can save a rejected manuscript.
Report it properly
State the test, the assumption checks performed, the test statistic, degrees of freedom, exact p-value, and an effect size with a confidence interval, not just "p < 0.05".