I've been doing the new mining for a few sessions now. It's quite a while since I tried the old style (in a Cobra), so can't compare very directly, but compared to sitting painting asteroids it's more interesting, and definitely more profitable.
Kit required: seismic charge launcher, abrasion blaster, prospector limpet controller, collector limpet controller, pulse wave scanner, refinery, roughly this equipment:
https://s.orbis.zone/1slb (I haven't set up the core modules, and my Krait has a fuel scoop because the hotspot I'm mining is about three jumps fully laden, so need to top up a bit), did similar outfitting on an Asp for the first attempt, only different is it will fit less. The subsurface missiles and mining lance are not very useful if going for cores, not sure about rocky asteroids, but icy ones with cores (and void opals are the most profitable, but there are others that are worth collecting too) tend to have accessible deposits that are not worth collecting, water, methane clathrate and the like. Use the DSS to scan the ring for hotspots, drop in on your chosen hotspot, avoid other ships and start pulse scanning for asteroids, the ones that show up have one or more of: cores, surface and subsurface deposits. Eventually you'll recognise the ones that can contain cores, and if you look close enough you can spot fissures, you can even use seismic charges without a prospector limpet, but that takes practice, is relatively slow (you have to get close to identify them), and some fissures are subtle, so I'll hit likely asteroids with a prospector.
Limpet conservation. Limpets are cheap, so fill your hold when heading out. Or nearly fill it; on your first couple of cores you might have to make space for minerals. Higher grade limpet controllers last longer, a limpet from a 3A collector controller lasts 12 minutes if nothing bad happens to it. Save your prospectors for likely asteroids, launch collector limpets after asteroid detonation, and manoeuvre round the outside of the expanding cluster to encourage your limpets to pick up nearby fragments without picking through boulders which can trap and destroy them. Keep slow when limpets are incoming or they'll crash into you and die. Thrown out fragments are often in clusters, get close to them and this will shorten the limpets' journey. Also pick off exposed surface deposits with the abrasion blaster from outside as you get line of site to them. With luck they drift out making the limpets' job easier. Don't be afraid to scoop a fragment or two yourself if that's all that's left rather than sending a new limpet after them. You may well still have your limpets following you after cleaning up a core, let them keep up with you while searching for the next mother-lode asteroid (haven't really found I need to go slow). If you back off to about 2km in time for the seismic charges to go off then they should survive. Doing this I've so far found I need to throw away limpets as I go.
Seismic charges, haven't been keeping close track, but estimate I use about 1/3rd the magazine to fill 96t in a Phantom, so with a bigger ship you may need another launcher if you don't want to make a return trip to reload after about 200-300t. Then again (considering the extremely high credits per hour, I'm not complaining), it does take a while searching for the next mother-lode asteroid, so unless it's possible to find them more frequently (maybe I'm not in a very rich ring), you may find collecting 100t is as long as you want to spend on a single session. (If you want to log out and back in mid-mining, be sure you've got enough boost to get out of scanning range of auto-spawned ships after log-in.)
Considered a Krait Mk II and fitting a fighter bay, might be worthwhile if I didn't need the fuel scoop, but with weak-ish shields it doesn't seem worth looking for a fight. The similar loadout (no bay, but scoop) on a Krait II will hold 128t to the Phantom's 96t.