If you are just starting out and have a smaller ship recommend doing surface laser mining of asteroids until you can get a larger ship that can do deep core mining, I personally love using an Imperial Cutter vs a Type 10 but the Imperial Cutter requires you unlock it with imperial ranks first whereas the T-10 does not.
Collector limpets are a must to auto capture the mining fragments, and having enough materials that you can synthesize extra collection limpets on the fly if you run out is also a huge plus. If you aren't running a well defended ship then having a fighter bay with an experienced NPC fighter can help you out from the random pirates that can jump in or attack you while you haul off your cargo to sell it.
I used to love spending hours doing deep core mining for low temp diamonds, the explosion the asteroids make when you set the charges is such an experience, just make sure your ship is far enough away so it doesn't get toasted.
See my video of deep core mining explosion
