There was no single "English" invasion and conquest of Ireland (historians prefer the term "Anglo-Norman"). Prior to the first "invasion", in 1169, Ireland was hardly "united": more like a series of regional "kingdoms", like Ulster, for example. I put the term "ivasion" in inverted commas because the first Anglo-Normans were invited in by Dermott MacMurrough, exiled King of Leinster, to help him reclaim his title. Of course, the Anglo-Normans then got greedy and gradually took over most of the country. Ulster remained more Gaelic, the least affected by anglicization: partly the reason it was "planted" with Protestant, loyal (to England/Britain) settlers, in the 17th century.

The best known of the early invaders was Strongbow, Richard Fitzgilbert, Earl of Clare (died 1176), who landed his force at Waterford in August 1170. After that, it was pretty much downhill all the way for the Irish, until the Republic was declared in 1948.

Before the Reformation however, the wars were mostly about power, status, wealth. When England (as it still was) adopted the reformed Protestant faith in the 16th century, things really got complicated. The old Anglo-Normans, pre-Reformation, had largely become "more Irish than the Irish", adopting Irish culture and language. The later Protestant settlers didn't. Largely speaking, they wished to retain their English/British, identity.

I'd suggest that you buy a decent history of Ireland.