How prevalent is the idea wherein characters have to keep earning cash to pay for their spaceship?
Is it central to character creation, what about afterward, when the game starts?
It's not really central to character creation - even if you try to max out ship shares you are unlikely to have a character who can refuse to play ball because it's "their" ship (with the possible exception of a loaned scout ship).
In game, having mortage/maintenance/npc crew salaries to pay helps the GM maintain that 'firefly' feel to the atmosphere - if you don't keep paying and doing maintenance, the ship starts falling apart. If you don't pay crew salaries, you'll find yourself short-handed or lacking a crucial skill. If you don't pay mortgages, your creditors will come after you.
All this is going on in the background, and the trading system makes almost, but crucially not quite enough to stay afloat. Which means that every so often, the players will have to accept a mission under-the-counter from a patron they'd really rather not do business with if they weren't down to their last few creds...
...It's the counter-balance to the freedom traveller players with ships get. Unlike a D&D party stuck in a region with a war brewing, or whatever, the travellers can get back in their starship and be on the other side of the bleedin' sector within a month. You can't force them to interact in a place which is clearly dangerous and they're clearly at a disadvantage because they can always fly off. It's that looming threat of running costs and debt which gives you the carrot (or stick) to make them (occasionally) do what you want to.