Have you gotten the "Back to School", "School Graduation", and "Higher Studies" research projects? Those are the core ones that lock off major portions of the tech tree. Check the requirements for whatever the next one is on the
tree viewer and figure out what you're missing.
Note that if you have "Plotting" but not "Pillow Book", then the next step is to manufacture a Pillow Book (which requires a Library) and research it. Many people get stuck here. You can continue to create and research pillow books to get a wide variety of techs.
Diplomacy is also vital (you'll need it for School Graduation), since you need it to interrogate and break people, necessary for many research paths.
You might also look at the requirements for "Laser Weapons Construction" and figure out what you're missing from there, if that's what you're aiming for.
Also note that there are many weapons you will never be able to assemble (you're, ultimately, pirates, not an international government organization.) I don't think there's any way to ever be able to build your own personal-scale Gauss weapons, for instance. You're pirates; some things have to be looted.