Congratulations on finishing!

Taking the time to assess, save and consider your next step is already pretty smart. I'm not intimately familiar with Ireland (as opposed to the UK), but it's likely you'll need to think about a masters degree before embarking on a PhD. If you're thinking of doing a PhD, I would recommend looking for somewhere you an do a Masters by Research. In the UK at least, this is essentially a mini-PhD. If you already know what you're interested in, it offers a few advantages: a taste of full-time research (ie do you even like doing this kind of thing over long periods?), a closer supervision relationship and often an easier path to a high mark (dissertations are easier to do well on than coursework, usually). Above all, it's a statement to anyone deciding on PhD funding that you are dedicated and able to carry out research to a high standard. You may even be able to publish the research, which is an even bigger advantage. Gaining funding for the PhD is a huge advantage - it's no guarantee of a good or easy time of things, but it helps a lot. Shop around for universities that offer good funding packages, and do your best to make yourself an attractive candidate for he committee deciding on who gets what.

Teaching will certainly not be irrelevant experience! But I would encourage you to shop around a bit and trying to make connections with potential supervisors elsewhere. While there may well be excellent reasons to stay with your current institution, its still probably worth seeing what alternatives might be out there. At the very least it never hurts to make connections with people whose research you like.