Murphys that emigrated to Newfoundland

My paternal lline all were of Irish descent and living in Newfoundland (Carbonear area).  I was told (by family still in NL) that the Murphys in our family were from Ballycotton, Co Cork.  Both of my great grandparents were Murphys, both born in Carbonear NL.  (Michael and Ellen).  I believe Michael's father may have been born in Ireland:  William Murphy (b @1815)  he married Margaret Connors (b @185) in Carbonear.  I believe Ellen's father David Murphy (b @ 1830) was born in Ireland and her mother's parents (Wliiam Dawley b@1803 and Mary Kenny b @ 1805) were born in Ireland.  So, I know my family lines originate in Ireland, but I don't know where to begin.  Newfoundland records are scare and don't list where in Ireland they are from.  So many Murphys from that area.... how do you tell that the "Michael Murphy" you see is yours?  I have taked DNA tests, which indicate that my strongest Irish origins are from Munster and West Kerry.  I am coming to Ireland for my 50th wedding anniversary and would love to know where my ancestors came from.  Any help or direction on how to begin would e greatly apprecialted. Many thanks.....