No birds... They are not family pets.
You need a pet that will fall asleep on the couch with your kids while they're watching a movie. A real companion. Birds are not companions. That narrows your choices to dogs or cats. While I would love to have a dog, I don't want the burden of walking it, and don't have the time for outdoor play that every dog deserves. So, I prefer cats. They use the litterbox. They can play indoors. And they love being the queen of the house. If you select a cat or kitten, be careful not to get one who hides from people. The first few we saw when we were looking for a new kitten tried to run under the furniture, and hide from people and activity. The kitten we chose was resting in her "cage" and when we walked up she looked out and meow'd at us. She was and is very social. She sits on my lap when I watch TV, on my desk when I'm working on the computer, and literally sleeps on my head every night. When company visits, she's right in the middle of the action, or close enough to monitor everything that goes on. Dogs are still the best, but given my schedule, a cat was a better choice.
Good luck!
PS. Personally, I recommend immediately replacing a pet when you lose one. Too many animals need a good home. To let yourself be sad over pet-loss only makes you very miserable. But you can quickly turn that personal misery over pet loss that we all put ourselves through, into love for a new, cute little puppy or kitten.