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Short Answer
In the absence of other constraints, a q-value threshold of 0.01-0.05 is traditional. A q-value threshold of 0.01 implies that 1/100 of the significant results are actually null.
Long Answer
q-values are a multiple testing correction to p-values. q-values provide more statistical power then a simple Bonferroni correction, but are still conservative. Where p-values estimate the fraction of null results that are classified as significant, q-values estimate the fraction of significant results that are actually null. The q-value for a result is the minimum false positive rate for all results scoring at least as well as the given result.
All thresholds are to some degree arbitrary. You should consider what is the largest false positive rate you are willing to tolerate in the features you accept as significant. This may depend on the difficulty or expense of wet lab experiments used to follow up your MEME Suite results.
Further information about q-values:
Statistical significance for genomewide studies Storey JD, Tibshirani R Proceedings of the National Academy of Sciences of the United States of America 2003 vol. 100 (16) pp. 9440-5