Hi, I'm not Irish, but I do know some engineers from Budapest who took a job in Galway :-)
Average full-time wage in Ireland is €45k, so you would be on decent pay relative to locals. Prices don't differ massively around the country (except house prices) but Galway is not particularly expensive.
If you're normally resident in Ireland, and/or an EU citizen, you get the same healthcare as locals, which is either free or requires some small fees to be paid (typically around 50 euros to see the doctor, for example). I wouldn't expect you to need to pay anything for your wife in terms of pregnancy and your child gets free GP visits until the age of 5 or 6. Private healthcare allows you to jump the queue for some things, get a nicer room in hospital if you stay overnight, that kind of thing. Or it may provide some benefit payments if you can't work because of illness (can be important for self-employed workers.) Most people don't have private health insurance, although the numbers are rising.
You would get child benefit €140 a month, I think.