What I'm recommending below isn't how I learned Irish, although I have used all of the resources listed in one way or another over the years. I suppose you could say that this little learning programme is how I would do it if I had to start from scratch again, and had no attachment to Donegal.
For the absolute beginner with no attachment to any particular part of Ireland I earnestly recommend beginning with the dialect(s) of Conamara, the dialect of Cois Fhairrge in particular. The reasons are laid out by Mícheál Ó Siadhail in his book
Learning Irish.
Two hundred years ago a good speaker of Irish, travelling slowly from Kerry to Antrim (and on to the north of Scotland), could have spoken the language all the way and noticed only minute dialectal changes as he passed from place to place. One dialect shaded into another in the most gradual fashion. Today, however, the Irish-speaking areas are separated geographically by wide stretches of English-speaking territory, and their dialects would seem fairly distinct to a man going from one Irish-speaking area to another. A good speaker of any dialect can, with a little practice, understand any other fully, but the old linguistic and communicative bridges between them have fallen, and they have tended to drift apart. We may hope that this drift has been stopped in recent years by broadcasting in Irish and by increased social contact between people from the various Gaeltachtaí.
In such circumstances, what sort of Irish should one teach to beginners? A dialect must be used, for though there has been one Official Standard of Irish spelling since 1945, there is as yet no standard pronunciation. No one dialect, however, has established itself as socially superior. A choice must be made.
The Irish in this book with regard to pronunciation and grammar is based on that of Cois Fhairrge, Co. Galway, and the necessary vocabulary is that which might be expected from a native speaker who has assimilated a modicum of newly-coined terms. The dialect of Cois Fhairrge has some decided advantages for the learner, since it has a relatively large number of native speakers. Furthermore, it has been more fully described linguistically than any other dialect.
In addition to what Ó Siadhail says, Conamara lies between the Ulster dialects and the Munster dialects and its central position makes it easier to cope with these than say an Ulster speaker trying to figure out what a Kerryman is saying and vice versa.
The first item on the list is a must-buy and keep handy forever.
Learning Irish by Mícheál Ó Siadhail (Yale). This book teaches the dialect of Cois Fhairrge through grammar and not by parroting. I think that makes it unique in Irish learner materials. (Art Hughes is trying the same for Donegal but all his stuff hasn't yet been published.) Get the CDs as well; they are
essential. The book comes with a pull-out at the back on Irish pronunciation. I say, start there and master it before going any further regardless of how long it takes. If you don't master Irish pronunciation from the start only other learners will understand you, and you can expect nothing but blank looks from native speakers. There is a free workbook by Nancy Stenson that goes with it.
http://phouka.com/stenson/LI-01.htm
More pronunciation:
http://www.fuaimeanna.ie/en/Recordings.aspx The website is free to use, but the book costs money. Not a lot of point in buying the book straight away since it's written entirely in Irish. Use the middle column for the pronunciation of An Ceathru Rua. It's great for nailing down a particular sound that you might be hearing in the other recordings.
https://routledgetextbooks.com/textbooks/colloquial/language/irish.php Again, recordings are free, books are to buy/borrow/steal. I'd suggest downloading all the audio right from the start and listening to it constantly in the background during the months you are working conscientiously through
Learning Irish. Perhaps look for copies of the books in a library when
Learning Irish is finished; they are no substitute, but a useful supplement, not to mention good preparation for a visit to the Conamara Gaeltacht.
https://www.focloir.ie/ Get the free app. I don't think dictionaries are too much of a help for the total beginner in Irish (just stick with the vocabularies provided until they are fully assimilated), but this dictionary provides pronunciation links for most words in all three major dialect groupings. Just click on the C for Connacht and you'll get something useable for Cois Fhairrge.
Listen to programmes from Conamara on Raidió na Gaeltachta
https://www.rte.ie/radio/rnag/
Look for
Ros na Rún on Youtube. Some of the early episodes contain a bad mixture of Irish and English in an attempt to reflect how a lot of Irish speakers actually speak. Just ignore the
Béarlachas and look out for the good Conamara speakers. It's a soap which contains all the usual stuff - murder, rape, coming out, euthanasia, infidelity, incest, theft, slander - everything you've seen on your own local soaps, only in Irish. I don't think they've done cannibalism yet, though. To reflect the local culture there's even a dodgy priest who... well, watch it for yourselves.
More money: If you have cash to splash buy
Leabhar Mór Bhriathra na Gaeilge by AJ Hughes. It's expensive, but worth every penny. It's your usual paradigm verb book for learners, but Hughes has taken the trouble to give complete examples in the Ulster, Muster, Connacht dialects, and in the modern standard too.
Do not buy the abridged edition. This gives only the modern standard and that would just confuse a learner using the above texts. To be fair, the abridged version is a godsend for schoolkids doing the standard language at school rather than lugging around the tome that is the full version.
When all that is done the learner should be ready for a visit to a Gaeltacht Summer School.
http://www.colaistenaomheanna.ie/ https://www.colaistegharumna.ie/
Advanced:
The Irish of Cois Fhairrge, Co. Galway, and,
Gaeilge Chois Fhairrge, An Deilbhíocht, both by T. de Bhaldraithe. These are both mid-20th century academic studies and definitely to be borrowed rather than bought except by the clinically obsessed.
Last piece of unsolicited advice: Don't try to express
yourself in the learning stages. That can wait till later. Instead, listen to how native speakers express
themselves in everyday matters.