Hello Fishnutt90804,
To answer one of your queries, there aren't any ships passenger records for those who went from Ireland to England.
Maybe if you give some more detail about your ggrandfather like date of birth, children's names and their dates of birth, etc. someone more familiar with England research can help you regarding England records.
Generally you would research back from your grandparents to find information about their parents, i.e. your ggrandfather's generation. The methods to do that would be to find your grandparents civil and church birth, baptism, marriage and death records, obituaries, cemetery records, tombstones which should give you informatiuon about their parents like places of birth, possible siblings, etc. to help you go back and research your ggrandfather's generation.
Regarding researching in Ireland, there are no census records before 1901 which isn't computerised, no bmd's before 1864 except Protestant marriages starting in 1845. None of the Irish bmds are computerised.
To find your ggrandfather in Ireland, you'd need to find his parents names, date of birth and place of birth in Ireland which is the town/townland, civil parish and county. With that information, as well as his religious denomination, you could then find out what religous church records are available for that location and how they might be accessed.
Regards.
Eilis O'Hara