There isn't really a universal answer to "which distribution fits best", because there are an infinite number of different distributions. You can compare the fits of various standard distributions using MATLAB's DistributionFitter app.
If you want to "fit a Gaussian", just compute the mean and std of the sample scores. Once you assume it is a Gaussian, there is no additional fit-relevant information in the sample beyond those two numbers.
By the way, this is a 'univariate' distribution rather than a multivariate one, because you only have one type of score--though you have many different samples of it.