Some one else already mentioned this, but there are are 3 main sources of income: bounties, exploration, and trade. I don't think you need to over-specialize for any of these, but understanding what makes you better at each of them lets you improve your fleet. It may be simpler (in terms of learning game mechanics) to pick one and focus on it, but I find it's often more efficient to mix and match as opportunities arise.
For combat, the only way you will make good money is by killing bounties, and you really need to scale your fleet to the available bounties, otherwise your supply consumption will be too high. System bounties will mostly involve fleets of frigates and destroyers, so you really don't need anything cruiser sized or bigger in your fleet. For person bounties, you want a similarly sized fleet to the bounty, maybe a little smaller or larger depending on your skills and piloting ability. If the bounties you see have no cruisers, then you shouldn't need any yourself (and same with battleships). As you become better at the combat layer, you can get away will smaller and smaller fleets. I would highly recommend storing the legions you have until you start seeing bounty fleets with capital ships. Officers are also very helpful for combat so consider hiring some.
For exploration, fuel efficiency is super important. Be every careful to check the d-mods on your ships and avoid the worst ones. Degraded engines and increased maintenance are killers unless you have the skills that mitigate d-mod penalties, and I would immediately trash any ships with those hull mods. Hull mods that reduce sensor range or increase sensor profile are also pretty painful since everything will see you before you see it. Low tech ships also tend to have higher fuel consumption so it can be worth avoiding them for exploration. Finding the surveying equipment hull mod and spamming it on civilian ships in your fleet can make all surveys cost 5 supplies, which is very helpful. Also make sure to put militarized subsystems on civilian ships. The skill that increases salvage also helps a lot for exploration. I would recommend trying to find 2-3 exploration missions to do in the same area, and then explore some of the surrounding systems looking for stations and wrecks to loot. New missions will have popped up by the time you return to the core. You really don't need a ton of combat ships to explore, so unless you're mixing in bounties on your trips (i do recommend this), you can significantly reduce the size of your fleet. You will want lots of cargo and fuel space though, so grab some tankers and freighters.
For trade, you will not be able to make money by trading on the open market. The only way to be profitable simply buying/selling is to deal in high value commodities on the black market. You will need to approach with transponder off, so understanding the sensor mechanics is key here. You can also make money by doing trade missions that are given in the bar. The value of these is based on the amount of cargo capacity you have, so if you buy lots of freighters, you will get offered much bigger cargos that pay a lot better. You can make all of your money just doing these if you want. You can also cheese the game a bit by raiding small worlds (such as donn) and knocking out their space ports. This will create lots of shortages and missions that you can make money off of.
