for no-hassle money, just head for the Colorado system.
The asteroid field between the New York jump gate and Pueblo station is classed as a mineable zone. Fly in there, park your ship in an empty patch of space, and start shooting all the small rocks that come by.
Every so often, one of the asteroids you blow up will drop a chunk of silver. Tractor it aboard, and you have silver that you never paid for.
It's best to use a single weapon for this. if you have more than one weapon on your ship, then different projectiles travel at different speeds, which means you may blow up a rock, and then blow up the silver that comes out of it as well, which is very annoying.
having procured as much silver as you want, sell it at a MASSIVE profit. Early on in the game, the best place to sell silver is California Minor. Later on, if you have the time, you should sell it in New Tokyo for more than 1,000 credits per unit.
Be warned that the silver is rare, and you'll spend a lot of time not getting anything from it, but if your patient enough, it does work, and you make big bucks.
This technique works with any asteroid field classed as a mineable zone. You can get silver, copper, water, and all sorts.