Elite Status

Ships gain XP as they perform in battle and kill enemy ships. Capitals, and especially Titans, are super expensive so you'll want to be keeping them alive to fight for longer anyway - but they can also be heavily upgraded to make them more powerful and resilient.

One way to help the grind for a ship is to place it near an ally's planet, where that planet is a popular route for a nearby enemy faction. Your capital ship will benefit from the ally's defenses, and will still pick off kills from the continuous stream of enemy ships. A capital can be pretty much left to its own devices in this way.

Or, the more normal method would be to have a roaming fleet of your own, dominated by a Titan and/or some capital ships, and use this single fleet to roam the star systems battling enemies. Just be careful in this method to keep the same ship(s) alive long enough that they can reach level 10 - e.g. if you've got one chosen ship (perhaps the one you start the game with), then pull it to the back of the fleet when it gets damaged so it has time to recover.

If you haven't unlocked it already, you'll get it automatically for And Who's Stopping Us? so pick the Titan to level if you can. Otherwise you will also get it on the way to Experienced Crewmen.