Several hours later...
Bloody hell, that was an exercise in frustration.
After reading several help guides, I still have many questions borne of frustration. Questions like
"Why are asteroids on the wave scanner brighter when they're far away?"
"Why does every scanned asteroid flash in two different patterns? Which one is significant?"
(Some folks are talking about orange and green, some folks are talking about orange and red, some folks are talking about black squiggly lines, it's all very confuzzling!)
and
"Am I crap at this because my colour perception is faulty (which it is) or am I crap at this because I'm new?"
So, I managed to find about one asteroid with a core, per hour of flying. Three asteroids, in three hours in a ring. Clearly I'm doing something very wrong

.
I investigated pretty much every single asteroid that lit up any colour other than blue and all but three were coreless, like a pinapple being used to serve a pina colada.
When I did find one with a core, I managed to do quite well. I went into an Alexandrite hotspot and came out with a bunch of Alexandrite, Grandidierite, and even some Void Opals (!). I still ended up leaving the belt with a mostly-empty hold though.
Still, I got my feet wet, and managed to blow some rocks up, I'm even getting pretty good at getting the explosive yield in just the right place to split them without atomising them, so there
is that.
And at the end? I made a healthy 20,433,523CR. Pitiful for three hours' mining for an experienced miner, but I can see how I might get to like this once I get better at it.
Anyway, some sparkly pics of the new ship

.
It's a pleasure to fly

.
EDIT: Filthymick was definitely correct on at least two points: I got scanned on my arrival in the ring, and as soon as they found I had an empty hold, they buggered off. Three-hours pirate free, which I'm very glad about. Mining is (at the minute) frustrating enough without being interrupted.
And second, yeah, the anaconda is way too big and unweildy for
this particular ice ring. Even flying something as "small" as the krait is like threading a needle in that belt!