Here's my fashionably late homework assignment!
It's hard to say what modern music I like because I've honestly never listened to many recent modern bands, and I dislike almost all of the top 40 pop/rap/country stuff you hear on the radio. I can name a couple bands from the 2000s I like, but my musical tastes are actually pretty wide. There's a good number of times I liked one or two songs from a band but wasn't as crazy about the rest of their work. These facts were true when I was high school-age, and they're still true now.
If I had to choose, I'd say my primary interest groups are classic blues/country (think O Brother, Where Art Thou? and Fallout: New Vegas), Silent Generation-era oldies/jazz, certain types of electronica (primarily demoscene/chiptune/vaporwave/synthwave/ambientish stuff), classic rock, and power metal - or really any metal that doesn't sound like the Cookie Monster having a seizure. Bands/groups/individuals that fall into these categories include Marty Robbins, Muddy Waters, Louis Armstrong, Vera Lynn, Sabaton, Brothers of Metal, Metallica, Skaven, Boards of Canada, Led Zeppelin, Jimi Hendrix, and perhaps Johnny Cash.
Game soundtracks deserve a special mention; they run the gamut but I'd have to single out distinctive indie OSTs with real work put into them, such as the soundtracks to Bastion and Into the Breach. The composer for Into the Breach, Ben Prunty, also made the music for FTL, and is in general a really talented electronic musician.
I also like classical music and traditional cultural music like Scottish bagpipes/traditional Middle Eastern music/Native American flutes, but I couldn't say as much about individual artists for that stuff, since I regard the music as more prominent than its performers in most cases. Russian composers like Tchaikovsky and Mussorgsky are some of my classical favorites that aren't super obvious and popular like Mozart and Beethoven. As for traditional cultural music, Clanadonia are great bagpipers while R. Carlos Nakai is perhaps the most famous Native American flutist.
As for what's "coolest" out of all that stuff for a high schooler, I'd have to say it depends. Best overall is a toss-up between power metal and 1930s-40s music: driving ballads about historical battles and Norse mythology are undoubtedly a strong contender, and a lot of it is pretty recent, but Great Depression and WWII-era music has an undeniable historical/elegant chic. Traditional cultural music is a decent pick, since it carries a worldly sound, and being of the same nationality or ethnicity as the stuff you're listening to is a potential conversation starter. As others in the thread have said, classical music is timeless and enjoyable, and not exactly trending with The Youth, apart from perhaps the most popular and super obvious artists everyone hears in music class. Electronica would be a great fit for a geek/computer programmer, while game soundtracks and more chill stuff like Boards of Canada would fit for both geeks and artsy folks. Classic rock and metal wouldn't be out of place for a shop class tradesperson, but I can't say it would be my top pick. Old country would have historical chic similar to WWII oldies, but I'm not really sure where blues would fit.