It's very exciting to hear you are planning a trip to the island!
A month is plenty of time to explore a lot of places around Ireland. Renting a house in these areas is a great idea so that you can make some day trips without worrying too much about changing hotels every day. I think the bases you chose are great. However, although Wicklow is amazing, it is only 1 hour from Dublin, so I suggest a city or town a little more south, like Waterford, Kilkenny, or Wexford. Also, is Northern Ireland not on your plans for this trip?
Here you can search for Self-catering homes
everywhere on the island and choose the one you like best for each base.
I would also suggest checking other types of accommodation
that Ireland offers.
Staying in a Bed and Breakfast is another great choice as the lovely hosts are a fantastic way to get closer to Irish culture and meet new people. They also have local knowledge that could help you discover new places that may not be on your plans.
I hope you find this information useful and let me know what you think of the B&Bs.