You can get up to 400 free ARX a week as a result of in-game activities, which works out as a basic paint every couple of weeks, or a more complex one every month. Depending on how many ships you regularly fly and what colour(s) you want them, that might be more than enough (is for me)I recently looked at painting my ships. The Arks required are thousands! So can there be another way to get my ship repainted? Perhaps based on rank or buy it with your in game credits?
There are a few cosmetics - mainly decals, but occasionally other things - which you can get entirely in-game: complete the tutorial, for an example, or check at the Tech Broker. There's also a set of rank decals which you get access to as your trade, combat and exploration ranks increase.