I have a black-box device with a modem attached (which I can send commands to), and would like to be able to connect to send data to a server from it. What connectivity options do I have, is PPP the protocol I need to use or is there a better option?
ppp is certainly the most common solution for getting an IP connection over a modem. There are other solutions, but there's no reason not to use PPP if what you need is an IP connection.
If you don't need an IP connection and you're writing both the client and the server, you could also do a straight serial connection from one modem to another, but that's kind of old-school.