Ships use 25% of their BP cost in MSP every year while anchored at a maintenance location. Fuel usage is based on how far your ships travel and how fuel efficient their engines are. Surveying and freighters are likely to be your largest fuel users in the early game, followed by military expeditions in the later game.
You can save a lot of fuel on cargo hauling by accepting slower freighters. Increasing the number of cargo holds can increase throughput faster than increasing speed does.
You can save fuel on surveying by making your survey ships slower and more efficient, as well as by being more selective. You could just survey planets and moons, for example, and skip the asteroid belts and comets until you actually decide to put a colony in the system.
For military expeditions, using an carrier with efficient engines to move fast fighters or FACs around might be better than building lots of fast destroyers.