Which of the following ports is the best one to use for a program I'm working on using a custom protocol still under development. I'm looking for one that will be accessible to virtually every host that is connected to the public internet (ie every host that can view websites can use this port). The three main options are:
Which of these is most widely accessible over the internet, including all isps, corporate firewalls, etc.
Not port 53. Toss-up between 80 and 443. If you make your protocol look sufficiently like HTTPS that a proxy will forward it the same way, then maybe 443 is your best choice.
All of those ports are used by well-known services, and you should use none of them (if your product is not a webserver or a DNS server.) DCCP Well Known ports SHOULD NOT be used without IANA registration. If your service is commercially viable or has benefits for the network as a whole, consider registering it for a lower port number: The registration procedure is defined in RFC4340, Section 19.9.
For experimental use, use a port between 1024 and 49151. Remember that even those ports should be registered with the IANA as soon as your service goes "live".
Regarding firewalls: You cannot predict if your service will be available to any network at all. Even if you use port 80, you probably will run against firewalls that do content checking.
As all the ports you've nominated are used for particular well-specified protocols, it's a very bad idea to use these for a different protocol. There's a convention that for a well-known port, there's a corresponding protocol, and if you break this convention, then at the least you're going to cause confusion, and at worst be suspected of nefarious intentions and be blocked. Martin's answer points you in the right direction.