Which town to book hotel at Amalfi Coast area in mid April?

Maybe Maiori. We were there in early May a couple of years ago and some of the towns were extremely crowded, the village of Amalfi was horrible.

Consider Salerno
Basically flat, has a sandy beach, less touristy, has train and ferry access

Avoid Amalfi, Positano and most of the small villages are steep with stairs and crowds everywhere

Does it have to be stroller friendly? Is a back pack at all possible? If this is the case I would suggest looking for which hotel will suit you best and decide from there. Sorrento might work better. It is not the Amalfi coast specifically, but has a larger flat section and you could still see the Amalfi coast , and is very charming.

Sorrento or Salerno, also for access to ferries, trains, buses. Boats may not run in April if weather or rough seas do not permit. Look for hotels that are wheelchair accessible. I think you can filter those on booking.com. Beaches in the area are not sand beaches, they are pebbly at best, if not cliffs and rocks.

Giving full consideration to your specifications, the best "answers" are Sorrento (which is not really on the AC), and Salerno, which is perhaps the eastern end of the AC, but is not a "rich folks winter resort", like Positano, or Ravello (which latter is not on the water). Salerno is much bigger than Sorrento, and more interesting and "Italian". You may need to choose more expensive lodgings in order to be able to walk to the water or, where available, beach.

You write "base". But you don't say what you want to "accomplish". Are you going to Pompeii, Naples, Capri, Paestum,or what? Do you want to imagine that you are residents of a picturesque Italian town, and go to a different restaurant in town every night? Have you looked at Google Maps yet? I would say that, from the AC, everywhere is a "long drive". It's simply impossible to "go places" other than your hotel town without a public SITA bus, a taxi, or a car-driver service, plus ferries when they are available (check start of the high season ferry schedule). Ferries are sometimes cancelled because of waves or wind, and they only run in daylight.

Certainly the worst town for a stroller is Positano. But I have to note that my mother had four children in NYC. She took us on the subway, lugging an umbroller milions of times. Sometimes I (oldest) picked up the front of the stroller for two sets of 18 stairs, sometimes we carried the baby.