Two days ago, I joined GOG and got both Freespace games. When I tried to create a callsign for single player, the game would only greet me with the menu that wants you to hit alt and tab for "disk space". No matter what I did even the CTRL, ALT, DELETE thing, it just wouldn't let me into the MAIN menu. Any insights?
PS. I've been looking all over the place without luck:(

Try FreeSpace Open. Nearly all problems with FS2 can be fixed by that. There's even a conversion that lets you play FS1 using the FS2 (and, of course, FS2_Open) engine.
Start here: http://www.hard-light.net/forums/index.php?topic=47640.0

Our anonymous friend is correct, don't even bother using the game as it is. The only reason to buy the Freespace games is to gain access to the assets for use within FSO.

Thanks for the tip. I'm almost on the verge of getting FSO. However, one snag that I think I now have is some sort of build. I got the launcher up but having a hard time selecting the build and having the launcher confirm it. The message is, "The launcher must be in the same directory as the binary you're trying to use. I wonder what I'm doing wrong?

There are several things you're doing wrong, apparently. The biggest mistake being posting about it here instead of on HLP.
In addition, something like this shouldn't havce happened if you followed the instructions I linked to to the letter; Should there be other issues, please join the #hard-light irc channel on esper.net (mibbit gadget link: http://widget.mibbit.com/?settings=b73fe961ed217d9a3cbd9637dc7ba9bf&server=irc.esper.net&channel=%23hard-light&noServerTab=false ), where we can troubleshoot your install.

In case it wasn't obvious from the thread that HELP_The E linked to, the easiest way by far is to use Turey's Freespace Open installer.
The link for the download is at http://www.fsoinstaller.com/files/installer/FreeSpaceOpenInstaller.zip
Be warned that this might download up to 5GB of content depending on what options you select, but this installer will do everything.
Once you're done and everything is downloaded, fire up "launcher.exe" from your Freespace directory. Choose the "Mod" tab, then load either the "fsport-mediavps" (freespace 1) or "mediavps" (freespace 2). Then hit "run" and you're good to go!
Note: I needed to move the FS1 movies that were automatically copied by the Freespace 1 installer before they would play - I had to put them into \Freespace 2\fsport\data\movies and I think they were in \fsport\movies.