I think these 2 previously answered questions will be very useful for you as you ponder testing for normality:
(1) how-to-choose-between-t-test-or-non-parametric-test-e-g-wilcoxon-in-small-samplehow-to-choose-between-t-test-or-non-parametric-test-e-g-wilcoxon-in-small-sample
(2) is-normality-testing-essentially-uselessis-normality-testing-essentially-useless
This answerThis answer has some especially useful info about test selection based on your N and what the tails look like of the distribution.
I would not recommend basing test selection on the results of a normality test. I would look at the data, think about your expected distribution based on the type of data you have, and follow the advice from above. A QQ plotA QQ plot can be helpful for 'eye-balling' if the data are approximately normal and test if a simple transformation of the data could help.