ION ENGINES:
The slowest, but most efficient propulsion type in use across the galaxy, the Ion Engine is a rare sight in most actual starships, producing too little acceleration to be effective for rapid travel, but instead sees most of its use on Mover Tugboats and as station keeping drives for space stations and satellites.
The fuel used by Ion Engines, usually noble gasses of higher atomic mass, are rarer and more expensive than the fuels for Chemical and Fusion engines (though far cheaper than antimatter), but they require a comparatively limited amount of fuel, allowing them to spend less mass and money on fuel for the same end velocity.
Ion Drives are more complicated and expensive than Chemical Engines, though less so than Fusion Engines, but having lower operational costs than either and have longer service lives, making them the most economical choice for propulsion.
CHEMICAL ENGINES:
The oldest type of space propulsion, the Chemical Engine has been the first propulsion system used by almost all races in the galaxy (with the exception of the Volus, which got into orbit using mass drivers and first used Ion Engines for propulsion). Cheap, moderately effective, and simple, any omni forge in the galaxy can pop out these drives in great numbers, and its fuel sources, while not as plentiful as the Helium-3 used by Fusion Engines, come in a great many varieties and are relatively common and simple to harvest (unlike Helium-3, which is majoritively stuck down the gravity wells of gas giants, or in ice that will yield chemical and ion fuels either way).
The Chemical Drive is used across the galaxy in nearly endless roles. A large number of short range vessels like Shuttles, Docking Tugboats, and Dropships use Chemical Engines alongside most short range missiles and torpedoes due to their compactness, low cost, and relatively high thrust. The main problem with Chemical Engines is that they require large amounts of fuel, making long range travel with them rather impractical at high speeds.
Most ships in the galaxy have Chemical Engines in the form of Reaction Control Thrusters, as Ion Engines lack the thrust to move a ship quickly while Fusion Engines are expensive, bulky, and more difficult to downsize (Antimatter Drives are out of the questions due to it creating the need of spending large amounts of extremely explosive material across a ship, alongside its high cost).
FUSION ENGINE:
The most common engine type for starships, Fusion Engines' relatively low fuel costs and high thrust make them the perfect commercial propulsion system, though the high unit price makes them rare in cheaper or expendable vessels.
The Helium-3 or Deuterium used on ships both for their fusion reactors and Engines is plentiful across the galaxy, though mostly trapped deep within gas giants, meaning that getting fuel is not challenging in most settled areas. Even in less populated areas or beyond known space, a full tank of fuel can take a ship far, at least compared to Chemical and Antimatter Engines.
Fusion Engines are expensive pieces of equipment, usually making up a significant portion of a vessel's total cost and being several times the cost of a similar Ion or Chemical Engine. They also have higher maintenance and operation costs than Ion or Chemical Engines, requiring specialist engineers or VIs and permits to be used in some areas of space, eating into some of the fuel cost savings. They also may have legally mandated lifespans whereupon they must be replaced, though this is less common, mostly being found in some of Asari Space and a few other areas.
Nonetheless, Fusion Engines remain prominent on Schooners, Long Range Missiles, Tugboats, Freighters, Civilian Cruisers, exploration ships, and many other vessel types. Some military patrol ships (especially Sloops and Corvettes) use Fusion Engines, but this is rare among major powers, as it lacks the thrust to match an Antimatter Engine. As of first contact, the Alliance's warships carry Fusion Engines as cruising drives for use outside of combat, saving costs on antimatter while still able to help in battle. This is mainly done due to humanity lacking the ability to create Antimatter Drives that can double as Chemical Engines.
ANTIMATTER ENGINE:
The rarest and most dangerous type of propulsion in common use, the Antimatter Engine provides extreme levels of thrust, for equal costs and risks. A ship with Antimatter Engines of equal size to another's Fusion, Ion, or Chemical Engines would have many times greater accelerations. However, most ships with Antimatter Engines have less mass dedicated to propulsion, using the saved mass for other systems while retaining a higher speed.
Some of that mass is definitely used for the near endless number of safety features a ship with an Antimatter Engine requires in most areas of the galaxy. Additionally, antimatter is far more expensive than any other type of fuel, even accounting for its thrust to cost ratio (being many times that of the H2/O2 used in most Chemical Engines, the most expensive per thrust propulsion system, while being an order of magnitude more expensive per kilogram). This leaves Antimatter Engines within the domain of only two ship types, the vessels of the super rich, and warships. Antimatter Engines are a status symbols for the wealthy among wealthy, showing their power through eating the massive fuel costs
In the final days of the Krogan Rebellion, a version of the Antimatter Drive that could also act as a Chemical Engine was developed, providing vessels using Antimatter Engines a low cost propulsion method while not needing additional engines. Such a technology has not been developed within human space, forcing human vessels with Antimatter Drives (almost exclusively warships) to either add additional engines (usually Fusion Engines) and fuel, increasing the total mass dedicated to propulsion, or spend the large amounts of money needed to operate a vessel with only antimatter. The former option is the usually choice for larger warships, such as Cruisers, Frigates, Dreadnoughts, and Carriers, but most Fighter types have only one type of propulsion in use, with those that include both commonly being outperformed in both cost and combat effectiveness against equal mass competitors.
The amount of antimatter a ship (especially a warship) actually carries is rather small, for a multitude of reasons: first, ships don't actually need much antimatter to operate for long periods of time (a fraction the mass of other fuel types they would need), so ships save tonnage, which can be devoted to other systems, by not carrying excess antimatter they most likely would not ever use. Second, antimatter is extremely expensive, so warships are designed to only carry the amount needed, ensuring that the loss of a ship won't also include the loss of a fortune in antimatter (less of a concern than the first reason, but still notable). Finally, most places across the galaxy have a legal limit for the amount of antimatter a ship (dependent on tonnage and ownership) can carry (excluding antimatter transports) due to concerns over extreme levels of destruction. A ship carrying a modest amount of antimatter blowing up is not too much of a problem (at least compared to a similar fusion engine ship doing the same), but a ship carrying tons upon tons of the stuff, that will cause mass destruction. It is also for this reason that antimatter transports are considered almost sacrosanct across the entire galaxy; a single such transport, if damaged, could cause mass devastation at a level no one wants, even the galaxy's worst.