Analysing Limited Data

For my thesis I involuntary have a small dataset due to a limited population. I was thinking about analysing this data with the statistical model ANOVA, using non-parametric tests or Bayesian statistics. What do you think works best? Or are there any other methods/models/tests I can use?
Any tip ore suggestion will be highly appreciated!
Thank you in advance.
Inge van der Borg
Utrecht University