As you grow larger, yes, logistics becomes A Thing™. So, as in real life, don't take your battleships when you're doing survey missions or fetch quests. Store your most cumbersome heavies and only bring them out if you're going in for a bounty that will require all hands on deck.
You can't always know, of course, so that's the risk you take but you save a huge amount of fuel/supplies if you're judicious with what ships you really need versus those you don't.
Late game, I take frigate fleets to explore the outer reaches. Nothing I can't stand to lose but high burn drives, low fuel costs, and a single Dram gets me just about anywhere I need to go.