Do you think it is important who buys/gifts the first doll (toy) for baby?
I don't think it's the who that BUYS the gifts, the baby won't really remember. I think it's important who PLAYS with the baby. Which should be mom and dad mostly. :)
I don't think who gave the gift first matters. Like Cassie said, the baby probably won't remember unless they keep it and play with it consistently for a few years. I think it's whoever plays with the baby the most often that they'll be more fond of.