I would not want a "t-top" if I was transporting an infant. That type of car is more of "sports vehicle," and not a "family car" in my opinion.
I recommend a 4-door sedan or larger family vehicle, depending on the size of your family. Also, check all the safety features (locks, windows, air bags, seat belts, crash test results, etc.) before making a purchase. You should utilize the Consumer's Report magazine or another reliable reference source to compare the safety ratings and reliability.