Ancestry does have the most people in their database but they are mostly American. If you are Irish and looking for Irish links, i.e. people who did not emigrate, then you might be better off with FTDNA.
Also, many of the sites allow you to upload your results to another site, either for free or for a small fee.
I tested a cousin with Ancestry but was able to transfer his results to FTDNA for free (though there may have been an offer at the time) and Myheritage (which is less than useless).