so the sound will be 'mensh chee-na
No.
Mężczyzna - Break it up into:
Męż - Czyz - Na
Men-ż-chiz-na - As per usual, the emphasis goes on the "iz" sound.
*The "ę" sound seems to be a matter of personal taste, but for simplicity in text I use the "en" form.
ivona.com/online/editor.php?tmpl=15 - Use this for pronunciation. Polish is much more linear in pronunciation than English, so it's pretty accurate. Just type in the word you want, select on the right Jacek, Maja or Jan, and press the play button. Ewa is very high-pitched and misses some key nasally sounds in Polish, in my opinion. For some laughs you can also type in Polish sentences and select a British pronunciation.