There are two schools of thought as to making maximum credits while mining. Both techniques require you to be in a Pristine Metallic ring.
1. Planet-eating. The goal here is to get in, stuff your hold and get out ASAP. Put a mining laser in every weapon slot on your ship, and fit as many collector limpet controllers as possible without limiting cargo space too much. You should only bring a few collector limpets, maybe enough for one full replacement launch. Prospectors aren't really necessary. Fly up to the first rock you see while launching your drone swarm, and just start blasting. Use all those mining lasers to suck the rock dry ASAP, and watch your swarm of limpets collect everything; don't be fussy, don't throw out anything. The goal is, as the name implies, stuffing your hold as quickly as possible. Rock depleted? Move on to the next-nearest rock and repeat. Leave as soon as the hold is full.
2. Rock-sniping. The goal here is staying in the ring until your hold is full of extra valuable cargo. For this you need a good prospector controller, and just one collector controller. You will need a very, very large number of limpets - filling about three-quarters of your cargo hold should be adequate. Check each rock one by one with prospectors, and ignore it unless it's full of goodies. When you find a rock, drain it, and then start firing off prospectors at other rocks while you're waiting for your small fleet of collectors to gather up the good stuff. If you scoop up unwanted junk, dump it and collect more valuable stuff instead. Everything below gold should be thrown away; many snipers throw away gold because it's not valuable enough and only focus on the PPP and other mining-only rares like osmium and samarium.
Which you use depends in part on the distance between the ring and the place you're selling the minerals; a planet-eater needs a short travel distance, a rock-sniper doesn't care. There's also available game time to consider; a rock-sniper could spend hours in a ring, and if you don't know you have hours to play, you definitely don't want to log off while you're in the ring. Otherwise, if you log back in again, a pirate will spawn and scan you. So planet-eating is better for the casual gamer, or for miners who are happy to sacrifice some min-max mining capacity for anti-pirate defence.
Rock-sniping is also what you want to be doing if you're going to be maximizing profits by accepting mining missions. Everyone agrees that mining missions seem to spawn much more frequently if you don't actually have any minerals in your hold, so many snipers stack up on a bunch of missions beforehand, then use those missions as a "shopping list" for their target minerals. Missions are likely to spawn NPC assailants, so you will need combat kit to take this option.
Planet-eating, on the other hand, is what you want to be doing if you've concluded that mining is worse than dental surgery and you just want to refine Selene Jean the Mining Queen's quota of refined minerals. Because it's quicker.
As for which ship, rock-sniping is more suited to smaller ships. I currently use an Asp for rock-sniping, though may buy a bigger ship and try planet-eating now that I've got plenty of cash to buy and kit out a large mining ship.