You can't trigger a state change during automatic assignment of a ticket. Obviously, if its a manual assignment, you can simply change the state.
The way we use it internally, tickets stay open when they come in and people are working on them. Once an initial response is sent, it is set to resolved or awaiting reply (there is an option to the left of the send button to select the state before sending the note to the user).
Once a ticket comes back when a user replies, it is automatically set to "In progress". You can change this in configuration\ticket content under Ticket states.