A just turned 4 year old child won't start school until September 2017. However that child will qualify for a free pre-school year under the ECCE scheme. That year is normally in a creche or Montessori, and is a 3 hour day.
Unless your children are 11 or over when you move, they will not get an exemption in Irish and will learn this as a standalone subject.
In general, there are 3 types of schools in Ireland - Catholic/Church of Ireland ethos, Gaelscoileanna where all subjects are taught through the medium of Irish (also non denominational) and Educate Together which are non denominational, non uniform and refer to the the teachers by first name.
Schools in Dublin tend to be oversubscribed. It may be easier to get in if your children are older. If you decide to live outside Dublin City it may be easier to get into local primary schools but you would want to keep an eye on secondary school admissions policy.
One thing that people moving from England find different is that we use workbooks rather than an endless stream of worksheets. You will get a booklist from the school and you will need to purchase the books, copies and stationery. Most schools will have a book lending scheme but that really kicks in later as for younger children they will need to write on the books. Many schools have a voluntary contribution system where parents donate money to contribute to the costs of running the school.
The school week is 25 hours (not including breaks) in primary schools. Schools vary on start and end times within those parameters. The first two years of school have a shorter day and end an hour before the rest of the school.
Commuting in Dublin can be a bit of a pain. If moving for work, I would suggest contacting people working in the company to get an idea about where people live and schools in the area.