The best items to mine from highest to lowest selling price is platinum - 19,000cr, palladium - 14,000cr, gold - 10,000cr and silver - 5,000cr. You can find all those in metallic rings and belts. You can also find silver in the metal rich areas.
You'll want to visit common, major or pristine reserve areas. Definitely stay away from the low and depleted reserve areas cause the time involved in mining is not really worth it. You will get between 8 to 12 chunks from a single asteroid. You can get 30% chunks from common reserves up to 60% chunks in pristine reserves.
If you don't mind being interrupted by pirates while mining, feel free to visit the belts or resource extractions sites. That's why it's usually best to drop into a ring away from the RES's. Pirates rarely if ever show up there, but you may run across another npc miner or two. If a planet has two rings to it, the innermost ring is the A ring and the outermost ring is the B ring when checking the composition of the rings from the system map.
If you can afford it, try to get at least a 6 bin refinery, that way you can keep the 4 best metals in there and use the 2 remaining bins for the junk minerals you'll get in the asteroid chunks.
Its also a good idea before selling your hard earned work to check the bulletin board to see if there are any missions asking for the mineral/metal you may have. You'll make more from those than selling it through commodities.
It can be a tedious job when first starting out, but I believe you'll learn to fly your ship much better as you chase down all the chunks. I can fill up my 72 slot asp in about 2 hours with palladium, gold and platinum, giving me between 500,000cr to a million.