Choosing Fisher's Exact or Binomial test for overrepresentation in PANTHER
For a guide on using the tests in PANTHER, see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6519457/.
In answer to this specific question, the defaults are the best choice (Fisher's Exact Test, with FDR correction). Fisher's Exact test gives more accurate statistics for relatively small counts (e.g. when only a few genes in your list are associated with a particular GO term). The FDR is a better correction to use for these types of analysis in general, especially given the large overlap between classes.
The other options are there mostly to support replication of older analyses, e.g. to replicate a published analysis that used the PANTHER over-representation tool prior to 2018, when the binomial with Bonferroni correction was the default.