I believe a developer mentioned that both Painite and Osmium are far more common in Resource Extraction Sites when they were introduced (along with Low and High Intensity RES sites). Additionally, asteroids in RES sites take longer to deplete and spit out more chunks than 'wild' asteroids do. I'll get the most chunks from an asteroid in a HIRES, followed by Low and Regular. Never tried to mine in a HazRES, but I imagine it's similarly rewarding.
I can generally find at least one 30-50% Painite roid when I mine in a HIRES site. This gives some incentive to mine in said sites, but at the same time one must weigh the risk of pirate attack when they do so. My Asp pulls over a million in with each 64 ton load, and generally close to half a million in bounties over a 30-40 minute period. While I had to sacrifice some cargo capacity for a good shield and a SCB, I am capable of effectively knocking out 'Condas and Pythons while at the same time efficiently sucking up ore (3 collector drones).
Generally I go for the higher quality stuff, and vent the lower quality ores while I mine. I survey a LOT, and only mine off of rocks that are primarily one of the big earners (Osmium, Painite, Gold, Platinum, Palladium, Silver), with trace amounts of other minerals. I'll drop an asteroid down by about 20%, and then quickly go to my refinery and vent whatever amounts of Bertrandite and Indite/etc before I get a full ton of it, and then knock another 20% off the 'roid before repeating. In this way, I inevitably end up with a hold exclusively containing the valuable stuff, and it doesn't take up any extra time, as I'm simply spending the minute or two I would wait for my drones to mop up after the asteroid is mined out mid-extraction.
If I see any opportune targets, I'll go kill them. If I'm scanned by a bad guy, I'll turn him into slag.
It earns decent income (Around 2-3 mil an hour) and is by far the most engaging and least mind numbing way of doing so I've found. It is, in fact, fun.