XtremePain that render of the eyes above is really noisy, it just seems like the convergence is too low or the time or the iterations are too low, but something is cutting off the render.
A lot of people don't realize that the order priority for renders is Convergence %, if that is not met by the time limit or number of iterations, then as soon as either time limit or number of iterations is reached the render stops too.
Another thing is the actual brightness of the scene, darker scenes have more issues with artifacts. lighter scenes also render faster.
One way to learn about lighting is to use mesh lights like
AlexStone mentioned, then look at photo studio setups using 3 point lighting, that will help you get a good idea of how lighting works.
Use this as a starting point, then experiment with adding more lights or changing light colors, etc.