Welcome to ocr.
Just about any decent DAW will have VST/VSTi support, so you'll be able to run the vast majority of plugins with that. There are lots of good free plugins, so starting with REAPER's unlimited demo and getting used to its workflow can be done without spending any money at all.
Komplete is excellent. I have a previous Komplete, and use something from there in just about every track I make. With my style of music, it's mostly FM8 and Battery, but for something fitting your jrpg-style intentions, I'd probably be using Kontakt a lot. I tried to figure out what exactly K11S contains, especially the Kontakt instruments, but can't find a page explicitly listing them. You get the "Factory Selection" with it, whatever that means. If it doesn't seem like you're getting the stuff you need from K11S, consider the standard K11. Also consider options from other developers, eg IK Multimedia and Magix. I use their stuff from time to time. But third-party libraries overwhelmingly focus on Kontakt, so if you're looking to expand your library later, Kontakt gives you a lot more options.
You say you're not interested in big orchestra, but you want to make FF/CT style music. You do realize a lot of that music is orchestral, right?
When it comes to the synth stuff, K11S should be fine, and there are plenty of good, free synth options available too.