Hi,
You will need either a "module" or a PIC with built in Ethernet controller and the a TCP/IP (or UDP) software stack. Microchips stack is in C and I'm pretty sure it's a no-go with PBP (I'll happily stand corrected though). Quite some years ago there was some work done on getting a software TCP/IP stack working with PBP, I don't really know anything about it or its current status.

With that said, writing, managing or even using such a beast is not a simple task as I'm sure you either know or will find out once you start looking at the amount of code required. It'll be SO much easier to use a module of some sort. I mean, if you're building thousands (or as a true learning experience) then investing the time in getting a software stack working might be worth it but for a one-off just use whatever module capable of getting the job done.

The only one I've got personal experience with is the W5100 chip from Wiznet. It's now pretty outdated (though I'm pretty sure it would work for this application) and the new W5500 looks pretty nice, there's a developmenent module available called WIZ550IO which is available from Digikey for less than 20 bucks. Now, this is still at a fairly low level and you need to write some code for it but compared to a software stack it would be like a walk in the park.

On the other hand you could get a module with the W5100 chip and pretty much just use the W5100 code that's available here.