You should book as far in advance as possible in order to ensure a smooth trip. The closer we are to the date of departure, the more possibility there is of not having any spare capacity on group trips.
Private trips are the same, in order to ensure a smooth trip it's best to book in advance. This way it's more likely you will get your guide of choice (if you have a preference) and not have any problems booking accomodation in Chernobyl.