Ireland TV networks are simpler than they look once you split them into broadcasters and platforms. I did this research last month when helping a relative in Cork pick an aerial setup, and the shape is this: RTE runs RTE One and RTE2 plus news and kids channels, Virgin Media Television runs Virgin Media One through Four, and TG4 covers Irish-language output, with Saorview as the free-to-air digital terrestrial platform carrying them all (https://en.wikipedia.org/wiki/Television_in_the_Republic_of_Ireland).
RTE is the public-service core, funded by the licence fee plus advertising, and its Player streams most output on demand. Virgin Media is the commercial challenger with a heavier US-import schedule. TG4 punches above its weight on sport and documentaries as Gaeilge. Saorview needs only an aerial since the 2012 analogue switch-off, which is why rural reception questions come up so often (https://en.wikipedia.org/wiki/Saorview).
Pay options layer on top: Sky Ireland and Virgin Media cable for premium sport and movies, plus the UK spillover channels many households watch via satellite. For my money, start free with Saorview and add one paid service only if your must-watch list demands it. If you are sorting out what to plug in where, this viewing setup walkthrough covers the aerial versus streaming decision better than I can in a paragraph.