I'll spare you the usual "don't get a Ph.D." spiel since you're coming from a position of financial security and it's not especially relevant for you.

It's not my area of specialty, but regardless of your field/subfield, my advice is always to look at who's actively publishing in your area(s) of interest, find out where they are, and see if they have a grad program. Obviously the standing of the program matters (over half of all tenure-track jobs go to graduates of the top ten programs) but so does fit with your advisor, and the best way to find an advisor who fits with you is to find out who's currently working in your area of interest.

Once you find the professor(s) who fit your area of interest, you can contact them to see if they're taking new doctoral students right now. Making this contact is important not just to make sure they're interested in you, but also because you need someone who will go to bat for you on the admissions committee. It's not a guarantee of a good outcome because graduate admissions are a crapshoot under the best of circumstances, but it's the best way to find someone who is a fit for you and who is interested in working with you.

The University of Toronto has a pretty big Celtic Studies department for undergrads and grad students. Not the US of course, but, at least when I was a student there, there were a ton of American grad students. They studied Irish, Scottish, and Welsh language and literature, in Old/Middle/Modern forms.

As everyone has already noted you probably shouldn't expect to become a university professor at the end. But as far as I recall, there were at least plenty of opportunities for the grad students to gain experience teaching undergrads, since there was already an associated undergrad program.

The previous comment is pretty much spot on re. the general way to approach a PhD. Partial disclosure: I do have a PhD in Medieval Irish history and I will just add this: it's a field in which knowing your way around languages is essential. If you want your work to be Depeding on which era you would like to focus, you would have to work around Old Irish, Middle Irish and possibly even a little bit of Modern Irish. Additionally you'd have to be comfortable around Latin regardless of the time period and, if you're studying something related to the English crown, even a little around Old French.

This, I cannot stress it enough, is hard. I worked primarily with Latin sources (which I like) and even then I felt like I needed at least the basics of Old Irish. Studying a language takes a lot of effort and a lot of time away from your main project. Personally, I ended up overestimating my abilities and, in the end, I had to let Old Irish go. I can't say if it had much impact on my research but it felt like a failure on my part. I would definetely suggest that you consider how much time and effort you feel you are able to devote to grammars, vocabularies and the like, if that is your chosen subject matter.

Other than this, I think you have a wide array of possibilities when choosing an institution and a supervisor. Do not limit your search to Ireland, the US and the UK. There is a growing interest in the field in Dutch and German universities too.