1. what types of cars have the lowest insurance costs for teen drivers, and
Thinking back to my teen years, it didn't seem to matter all that much. I imagine a good 80% of the cost is fixed, due to the liability of a young, inexperienced, male driver. Things that will run up the cost are high performance cars, two seaters (don't ask me why), and convertibles.

2. what types of cars are safest AND least likely to get damaged or totaled?
Modern cars are going to be the safest. Anything say 2000 and up will have airbags, side impact beams, crush/crumple zones, etc. But keep in mind, energy absorbing crush zones actually INCREASE the odds of a totaled vehicle in an accident. They protect you by deforming to absorb crash energy, but in doing so, they are one time use, if you know what I mean.

so far DF and I have been discussing things like Toyota/Honda small SUV's, for reliability....
Be careful of small SUVs with spare tires hanging off the rear hatch. Back into a pole or taller vehicle, and the rear window is often shattered. A rather pricey repair. In my experience, teens are rarely skilled at driving it reverse.

and now I'm actually picturing something like a 20+-year-old Mercedes Benz that won't crumple in the school parking lot.
If you have financial concerns about repairing/replacing a $4-5k vehicle, It is extremely unlikely that you will want to pay to keep a 20 year old german car on the road.

If it were my kid, I'd probably be looking for a basic Civic/Carolla maybe 8-10 years old. Find a clean one that hasn't been modded or beat on, and it should go 200k miles easy with very little money put into it.