The roads of the Midlands offer an easier intro to Irish driving than the hairpin bends of West Cork and Connemara. Because the area has a decent network of main arteries and off-the-beaten-track byroads, a car may be your best option for covering the widest itinerary.
Don't be surprised to round a bend only to confront a herd of sheep idly grazing with little hurry about them—do what the locals do, slow to a stop and wait for an opening in the woolly mass to occur. The same goes for cows. Refrain from honking your horn on these occasions—it will only confirm your status as an impatient tourist, and, besides, the cows won't take a bit of notice.