A mass effect drive core decreases the mass of a bubble of space-time around a ship. This gives the ship the potential to move quickly, but does not apply any motive power. Ships use their sublight thrusters for motive power in FTL. There are several varieties of thruster, varying in performance versus economy. All ships are equipped with arrays of hydrogen-oxygen reaction control thrusters for maneuvering.
Ion drives electrically accelerate charged particles as a reaction mass. They are extremely efficient, but produce negligible thrust. They are mainly used for automated cargo barges.
The primary commercial engine is a "fusion torch", which vents the plasma of a ship's power plant. Fusion torches offer powerful acceleration at the cost of difficult heat management. Torch fuel is fairly cheap: helium-3 skimmed from gas giants and deuterium extracted from seawater or cometary bodies. Propellant is hydrogen, likewise skimmed from gas giants.
In combat, military vessels require accelerations beyond the capability of fusion torches. Warship thrusters inject antiprotons into a reaction chamber filled with hydrogen. The matter-antimatter annihilation provides unmatched motive power. The drawback is fuel production; antiprotons must be manufactured one particle at a time. Most antimatter production is done at massive solar arrays orbiting energetic stars, making them high-value targets in wartime.
The exhaust of fusion and antiproton drives is measured in millions of degrees Celsius. Any vessel caught behind them will melt like wax in a blowtorch.
Any long-duration interstellar flight consists of two phases: acceleration and deceleration. Starships accelerate to the half-way point of their journey, then flip 180 degrees and apply thrust on the opposite vector, decelerating as they finish the trip. The engines are always operating, and peak speed is attained at the middle of the flight.