You don't need to grind money for a larger ship. Just find the buildings with a large antenna on top and search for crashed ships. They will be from -1 to +1 your ships slots. Then you can break down your mods in your ship for lots of resources and transfer them to the new ship if it's larger. Otherwise, you can swap to the new ship, break down its resources and go back to your current ship and look for another crashed ship.
I did that to get from a ~25 slot all the way up to a 48 slot ship. Now when I look at the prices to buy a ship, they're something like 400 Million.
Also, this game got me motivated to play Elite : Dangerous -- which I bought on sale nearly a year ago and never played. Elite makes an excellent companion to No Man's Sky as their strengths and weaknesses are nearly opposite of each other.
Thats what I did up to a ship with 30 slots. Can't do more, it's too boring.
Funny you mentioned Elite: Dangerous. I too have had that game for many months and was motivated to play it. Yesterday I fired it up, got about 10 mins into it, and quit. It's an issue with the controls. I just can't get used to them. Maybe an xbox controller is better for me.