Asics are good runners, but one type does not suit everyone. Asics have high arches, and gave me great grief when I was training for a marathon.
Do not trust the young staff in sports shops, most are clueless. Ideally, a running shop will have you run up and down the street, or on a treadmill, and see if you are a pronator, and recommend from there.
Also, I was not convinced about dry flo clothing until I bought it, no more soggy t shirts to give " joggers nipple"!
Get the shoes right. I have not bought runners in Dublin, so not sure where to recommend. If you are going to be in london, cardiff or edinburgh, "run and become" is an excellent shop with trained staff.