Closing on April 28th. What day should we request utilities be transferred in our name?

Our agent continues to be useless in terms of coordination/advice. What date should we request for the utility companies to start in our name? April 28th or April 29th? Not sure if it makes a difference that April 29th is a Saturday.

Also what language do I use to find out if there are outstanding bills on an account if the month isn't yet over? Like, say the owners are on a billing cycle of April 14-May 14, I imagine there would be "outstanding" costs for the 2 weeks they used the utilities.