In some stories I'm writing [and still shoring up for agent querying later on], I settled on two types of FTL. I wanted it to be as reality based as possible, in regards to what is physically possible for technology, and FTL techs I picked are actually the only 'rule breaking' techs I have. Everything else, such as spacecraft centrifuges, magnetically confined plasma windows and suspensions for hover vehicles, fusion, antimatter and biotech and nanotech, is all plausible.
But the FTL methods I selected are all theoretically possible. First is the good old Alcubierre drive, which requires exotic matter with negative mass to be collected, and a lot of energy, though less with better calculations and a warp bubble shape that's also being oscillated it seems. As is theorised in real physics, the ships that use them in my story have collected particles on the outside of the bubble that fly forwards when they drop out of FTL, so they have to be careful not to be pointing at whatever they're headed for, and it gets more powerful the further a ship has traveled in one single jump period. In world, this is a war-crime if its intentionally used in combat among the associated races and governments.
Second is not used for travel, not by my Tier 2 civilizations anyway. Microscopic wormholes are formed, and held open by tetrahedrons of exotic matter with negative mass in the middle of their throats. The tetrahedrons have gaps inside them, which is what restricts how big an object that traverses the wormhole can be. In my stories' case, they use them as beamed communication shortcuts, effectively enabling near live communications so long as you are close enough to a wormhole satellite, and it isn't too far from the chained ones and your recipient. Its basically a hyperadvanced telephone exchange of sorts, a spacetime bent fibre optic cable. Of course, I leave the door open for more powerful cultures they might find to use bigger wormholes, big enough to traverse, or big enough to fire weapons through, or even just big enough to act as interstellar peeping hole type periscopes from light years away.
The one white lie of physics I implement is the exotic matter, which is theorised as some form of concentrated dark energy or alike in actual physics, to generate the negative mass conditions to expand space and hold open a wormhole. So exotic matter is a valuable commodity, though one that has to be manufactured, as it doesn't naturally occur.