Hi Anne,
It's great that you're trying to find out more about your Irish roots!
Brian has already given you some helpful tips and suggestions, and I hope it leads to more information about your Cullen and Murphy ancestors.
Researching the
Roots Ireland database is a great idea to start off with. Once you have found out more about what county or area your ancestors were from, you can reach out to the right archive. Keep in mind that before 1864, records were kept in the form of
church and parish records, and all of the surviving records are in the care of county based
genealogical centres.
Keep us posted on your findings, and we're always here if you have any questions! :)
Wishing you the best of luck on your research,
Melin