The current version of the game doesnt really have insurance. Any ship you own will be replaced for free an unlimited number of times or you can pay a small fee to expedite it's respawn.
To make sure your ship is save you have to land at a starbase, outpost etc and then your ship is stored but sometimes you might spawn at a different base if your ship is stored somewhere that is over full of people. So you then have to file a claim on your ship so it is replaced at the base you are at now. Its confusing etc.
But for now, you dont have to worry about every losing your ship though you might end up at some places where you cant spawn your ship (like some of the planetside outposts only spawn land vehicles.)
You can buy some ships in game with in game money now but im unsure how the insurance works on them. If you buy a ship with real money and the insurance runs out (ie 2 year insurance and its been 2 years since the game went into FULL release v1.0 (which is when they will start counting insurance times)) they have said that you will still be able to retrieve your ship but it will cost more money than what buying in game insurance for it would have costed.
My personal opinion though is that you shouldnt buy any ship for real money unless it have LTI and even then, as of right now I dont think it is a good idea. But they also have a CCU open which allows you to upgrade your ship and keep that ship's insurance. so if you wanted to upgrade your aurora lti to an avenger that might be feasible.