I fixed the problem I was having. It turned out the issue was totally a port forwarding problem. I had forwarded the ports, had a static IP, but on my particular router it asks for the last digits of the new IP address, and those were wrong. Got it all figured out and it works great. Just used the method that comes built in to the game and had my friend Direct Connect to my IP.
As for the server application, from the description I would assume you could play on the same machine, but I could be wrong. I was getting close to trying it before the direct connect solution worked out.
Thanks for the reply! I'm thinking about posting an in-depth bit about getting it up and running from purchase to port forwarding to playing, since a lot of the links I found were to the old legacy forums (and therefore didn't work) or were to somewhat outdated info. Does something like that already exist, and therefore me doing it would be redundant?