Listen to a few sound files and see what dialect you like the best, heres some examples of native speakers from the Gaeltacht.

Conamara Irish: (Connacht Irish)
http://www.youtube.com/watch?v=A3-Z8U6WxVw

Conamara has the biggest Irish speaking territory in the country and far by the most vibrant Gaeltacht in my experience.

Donegal Irish (Ulster Irish), this would be the second biggest Gaeltacht in the country:
http://www.youtube.com/watch?v=EBgKAq9fPl0

Kerry Irish (Munster Irish)
http://www.youtube.com/watch?v=Sg0L0TrdowQ
The sports commentator speaks Irish from Corca Dhuibhne.

The interviewer speaks Conamara Irish.

Grma a Bhen ar son na videonnaí sin, cha rabh's agam CU Burn Tá sé deas Gaeilg nádúrtha Thír Chonaill a chluinstean Tchím go bhfuil mé giota beag as cleachtadh nó cha dtuigim achan rud

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Thanks for the videos. So in the third one the interviewer speaks Conamara Irish while the other man speaks Kerry Irish, right? Hmm... It might be just the way these particular people speak but it seems to me like the Kerry Irish sounds "clearer", like... the words would be easier to understand if I knew Irish, while Conamara Irish seems to sound more complex, although I might be wrong because I have no idea. But anyway, because I lived in Galway and I like Conamara (beautiful National Park, btw), and because it's kind of in the middle, I think I'd go for the Conamara Irish, yes.

Also, Conamara is like the "epicenter" of seán nos singing, right? That's also important for me, because I like it and it would be great if I could understand the songs.

This must be Conamara Irish, it sounds great: http://www.youtube.com/watch?v=qc_m9xd40yU

Although I now realize my favourite seán nos singers, Neill Ní Chróinín and Iarla Ó Lionáird, speak Munster Irish... damn... I'm not so sure of my decision now..

Yes that's Connemara Irish

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

From what little I've heard of Mícheál Ó Muircheartaigh, that's the way he speaks in English as well: very deliberate and unhurried. (At least in interviews; his sports commentating is a different story altogether.)

Aye, I don't think there are clearer dialects, it only depends on the person who's speaking. I heard people from Munster, Connemara and Donegal who speak very clearly, and others that are very hard to understand.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Oh ok, I see, thanks for the clarifications. Then I think I'll go for the Connacht Irish if it's possible. Do you know any good free websites (with audio files if possible) to start learning from scratch? If that's not possible and I need a book then I guess I'll have to buy it, even though my economy is not great at the moment.