How should one go about choosing a default TCP/IP port for a new service?

Go here and pick a port with the description Unassigned

First step: look at IANA listing :

There you will see at the tail of the list

"The Dynamic and/or Private Ports are those from 49152 through 65535"

so those would be your better bets, but once you pick one you could always google on it to see if there is a popular enough app that has already "claimed" it