A.V.
It depends on the denomination. Your responses will vary on the congregation. Some churches only baptize adults and only then upon membership. One friend had a hard time because her daughter attended a Catholic church, but the friend herself was agnostic and did not. She wanted a minister friend to baptize the child but he said that it would violate the rules of his church to do so for her since she had no church associations (he was not a Catholic priest). My own pastor met with us and talked to us. My husband does not generally attend church. I do. My pastor asked if we were doing it out of tradition or if we really wanted to present our child to God/the church and promise to raise her in our (my) faith. It was a thought-provoking question. One of the commitments you are making when baptizing a child is to raise that child to know God. Some churches require that as part of that vow, you have some association with their congregation before they will permit it, especially if the child is under the age of membership (an age where they can decide themselves). Since it is your hometown church, that association may give you a pass on these regulations but be prepared for it.
My DD's godparents were there and did stand with us, but it was not required. In Catholic churches, I believe it is.
There's also "secular" godparents and "religious" godparents. The secular ones are there for the child if you get hit by a bus. The religious ones help you raise the child in the faith. They can be one and the same, but sometimes they are not. (My DD's godparents are the same on both counts.)
Good luck in your search. You may discover more about yourself in this process, too.