In terms of "the classics", I think you've got the essentials down

Only things missing are either niche, or can be labeled otherwise: Queensryche, and Motley Crue, for example. I'd also throw in Metallica, but that's only really valid for the older albums.
As for my collection, I usually have my own labels. They're not really accurate, but they do the trick for me. Mostly, I fit bands that don't really fit under any other label as "modern metal". Meaning, it's just... heavy metal. Can't really call it anything else, except oddly specific subgenres that will lead you to a subfolder list the size of my arm.
- Body Count -> MODERN METAL
- System of a Down -> I have this labeled as "rock", but I'm not sure about it. Wikipedia labels them as simply "Heavy Metal", so I'd say MODERN METAL
- Metallica -> TRASH METAL (although, again, really only the older albums)
- Slayer -> TRASH METAL
- Disturbed -> MODERN (NU METAL, if you want to get specific)
- Slipknot -> MODERN (INDUSTRIAL, if you want to get specific)
- Megadeth - MODERN
- Pantera -> MODERN (GROOVE, if you want to get specific)
- Anthrax - TRASH METAL
It's tricky to get non-metalheads into metal, as it's a pretty specific genre with increasingly deeper and heavier subgenres. "Liking" metal is a matter of slowly dropping down into increasingly heavier stuff until you hit the absolute limit of what you like. Plunging in headfirst will just give you a distaste in general.
Usually, starting out with the classics is a good idea: Iron Maiden, Judas Priest and Black Sabbath (you've got these covered

). Diving a bit deeper, you'd still stay with the "clean vocals" bands, while getting a bit more modern with the riffs and beats. To start, I'd suggest some
power metal or
symphonic metal.
Again, staying with the classics is a good idea. Here's a classic power metal band (whose sound is pretty close to the OG classic metal bands):
Blind Guardian:
(their album Nightfall in Middle Earth is all about the Silmarillion, and is amazingly epic)
If you want to get a bit goofier, there's plenty of options. Power Metal is rife with "silly" bands, who take the concept of high fantasy, and just fucking run with it, laughing at themselves all the way. Dragons, timetravel, lasers,... nothing is too much. It's usually done completely over the top, on purpose. And it's freeing, in a way. Who cares about goofy when goofy is the whole point? It's just plain fun.