One suggestion is to estimate the time you'll need and double it. Nothing is worse than parents who announce they have something else to do in fifteen minutes. Keep in mind, you're not in charge, the baby is. The baby will do what the baby will do and you'll simply record it.

I have the 50-200mm and the 55-300mm. I just got the 55-300 a few days ago. Both are fine lenses. As to which is best, I don't know. They both give me good results but I'll probably use the 50-200 more than the 55-300. I don't shoot wildlife or birds and for shooting in the city the 50-200 gets the nod. There are special occasions where I will use the 55-300 such as the sports parade later this month.