Hi, I have been to Goa many times and with my kid so as you are going for 1st time. I suggest you to stay in North Goa near candolim or vagator beach. Always find a resort or hotel which is walking distance from beach. At baga beach you will get many pubs where you can go with baby. Full day enjoy on beaches. You can rent an activa or car in self drive and visit places easily. There are many famous church and temple which you can visit.
Hope this information helps you