Seems like it's about as good as anything else: http://forvo.com/word/%D0%BC%D1%83%D0%B6%D1%81%D0%BA%D0%BE%D0%B9_%D1%80%D0%BE%D0%B4/#ru
As I understand it, letters in Russian consonant clusters adopt the voicing/voicelessness of the last consonant in the cluster. к is unvoiced (it's voiced counterpart is г). Hence, ж is devoiced, and is pronounced like ш, its unvoiced counterpart. Word final voiced consonants also tend to be devoiced; hence род sounds like рот.
Well мужско́й /mʊʂˈskoj/ has an unstressed first syllable, so that vowel is weakened to /ʊ/, the vowel in "put" or "should".
Make sure you're familiar with vowel reduction, it's at least as important in Russian as it is in English: https://en.wikipedia.org/wiki/Vowel_reduction_in_Russian