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

If by widely-used, you mean you want to protect against other people using it in the future, you can apply to have it marked as reserved for your app by IANA here

The most comprehensive list of official IANA port numbers and non-official port numbers I know is nmap-services.

You probably want to avoid using any ports from this list (Wikipedia).

I would just pick one, and once the app is used by the masses, the port number will become recognized and included in such lists.

Choosing an unassigned one from the IANA list is usually sufficient, but if you are talking about a commercially-released product, you really should apply to the IANA to get one assigned to you. Note that the process of doing this is simple but slow; the last time I applied for one, it took a year.

As others mention, check IANA.

Then check your local systems /etc/services to see if there are some custom ports already in use.

And please, don't hardcode it. Make sure it's configurable, someway, somehow -- if for no other reason that you want to be able to have multiple developers using their own localized builds at the same time.

If this is for an application that you expect to be used widely, then register a number here so no-one else uses it.

Otherwise, just pick an unused one randomly.

The problem with using one in the dynamic range is that it may not be available because it may be being used for a dynamic port number.

Well, you can reference some commonly used port numbers here and try not to use anyone else's.

If by "open to the public at large" you mean you're opening ports on your own systems, I'd have a chat with your system administrators about which ports they feel comfortable with doing that with.

Choose a number that is not very common

Choose a default port that doesn't interfere with the most common daemons and servers. Also make sure that the port number isn't listed as an attack vector for some virus -- some companies have strict policies where they block such ports no matter what. Last but not least, make sure the port number is configurable.

Use iana list. Download the csv file from :

https://www.iana.org/assignments/service-names-port-numbers/service-names-port-numbers.csv

and use this shell script for searching for unregistred ports:

for port in {N..M}; do if ! grep -q $port service-names-port-numbers.csv; then echo $port;fi; done;

and put 2 numbers instead of N and M.