Correct approach using t-test and Wilcoxon rank sum test? I want to compare 2 datasets. 
I have a biological structure A with its atom coordinates which are a few thousands. I also have from these atom coordinates the coordinates over time of about 20 nanoseconds. 
From this structure A I made about 70 simulations. After the simulation I calculated the distance between atoms within this structure and afterwards the average distance of these 70 simulations for each time step which means that I finally have the average distance of 20 nanoseconds of the structures A.
Now I also have a structure B with which I made 80 simulations and performed the same procedure as described above.
Finally I want to compare the average distance over time of structure A and structure B.
1) I make a Shapiro-Wilk or Shapiro-Francia test to make sure that the data has a normal distribution
2) If the data is normally distributed I use a t-test, otherwise a Wilcoxon rank sum test
Is this a correct approach? 
 A: Edited: "In large samples, the t-test is not especially sensitive to non-normal data." So the question you need to answer is whether your data are independently and identically distributed and use the t test if interested in "average distance".
A: (i) Since measured values over time will often tend to be correlated, you shouldn't assume independence without good reason. 
(ii) if your real interest is in 'how similar they are' a hypothesis test will not answer that question - it answers an entirely different question 
(iii) the goodness of fit test also answers the wrong question. If you're trying to decide how much the normality assumption could affect your inference, you should address that question.
The two-stage procedure "test for normality and if it's not rejected use normal theory procedures otherwise use something that doesn't assume normality" is not a good strategy. It has the problem that neither of the second stage tests has the nominal properties. That is you don't get the significance level and power characteristics you get when you don't choose which to do based on the outcome of the first stage test. If some procedure is acceptable to you when you don't have normality, and it performs reasonably when you do (like the Wilcoxon, which has very high ARE), there's no reason to avoid it if you're not reasonably confident of normality. If the slight loss in power does concern you, why not go to a permutation (/randomization) test instead?
[On the other hand, in large samples, a t-test may not be very badly affected by an amount of non-normality that is easy to detect, so it may be perfectly reasonable. Since you can simulate data, you have the ability to assess the impact of similar non-normality.]
