Okay, so here's what you should do. Go to
http://www.fsoinstaller.com/ and download the installer. This is a handy little tool we've made that you can use to manage your mod installs. Amongst the things you should tell it to install is "wxLauncher for Windows", which is a new Launcher that is fully compatible with modern Windows OSes. The Launcher you are currently using, also known as Launcher 5.5g, is obsolete and will not work with future builds of FSO.
The only other question I have really is what is the best order to play the Freespace campaigns in? When I launch Freespace 2 Open under select campaign I have a few available...
1. Freespace the Great War
2. Operation Templar
3. Silent Threat
So you are obviously running the FreeSpace Port as the active mod, in which case you should start with The Great War (which is the FreeSpace 1 main campaign). Operation Templar is entirely optional, and Silent Threat should be skipped; There's a much better version of that campaign called Silent Threat: Reborn, which you can get through the Installer I mentioned above.
If you have further questions, I would invite you to the #freespace channel on irc.esper.net (you can find a link to it under the HLP dropdown in the menu bar of this site), or to drop by the HLP Discord (found
here).