Per the documentation of the MuSiC smg module:

P-values and false discovery rates (FDRs) for each gene in gene_mr_file is calculated using three tests: Fisher's Combined P-value test (FCPT), Likelihood Ratio test (LRT), and the Convolution test (CT). For a gene, if its FDR for at least 2 of these tests is <= max_fdr, it will be output as an SMG. Another output file with prefix "_detailed" will have p-values and FDRs for all genes.

To report in a paper, use p-values/q-values from either CT, LRT, or both. CT performs slightly better than LRT overall, but LRT sometimes skips false-positive SMGs that CT picks. Hence the use of the max_fdr cutoff as described above.

It is perfectly fine to modify the q-value (FDR) cutoffs however you like, because background mutation models differ wildly between tumor types. Do a literature search on the highest ranked genes, and work your way down the list. When it seems like there are a lot of irrelevant genes, then that's where you draw the cutoff.