Video, best?

Before the nineties, there couldn't have been any "Russian music." There was Soviet music.

By the way, I spent a long time deciding whether to write "Russian" or "Soviet"... I settled on Russian. Turns out, that was a mistake. ;)
Yes, there was Russian music before the nineties. The USSR was only formed in 1922, but before that, there was Shalyapin, Obraztsov, and many others, and folk art... let's not argue, okay? We're not enemies, after all.

Can you give me a couple of examples? Preferably from different genres.

Okay, it's night now, so off the top of my head:
rock — Master immediately comes to mind, and mostly the lyrics by Kokoreva, not Yelin:
Beregis' (1987), Ne khotim! (1989), Palachi (1989), Naplevat' (1989)
Is DDT rock? I really love them, including their early albums. It's just that these lyrics are still relevant, and they're sung "without censorship," as they were later.
Inoplanetyanin (1982), Vsyo idyot svoim cherodom (1982), Vsyo khorosho (1983), Ya poluchil etu rol' (1988), Zmey Petrov (1991)
I wasn't particularly into Kino, but they have some good songs too...

Soviet retro (I'll include pre-Soviet here):
Zavetny kamen', Tri poradi (in Ukrainian), Raskinulos' more shiroko (this is from 1900), Kapitanы mezhplanetnykh korabley (strangely, it's a kind of brainwashing: different ideas are embedded), Ya lyublyu tebya, zhizn'.
If you need more, I'll come up with some more tomorrow with a fresh head.

Pop... hmm. For some reason, I remember "Kak rodnaya menya mat' provozhala" and songs by Eduard Khil.)

What is your attitude towards, say, rap or pop music? And why?

I started with pop music, of course (although, no, I actually have a classical music education, so I started with classical music). Well, in general, I used to listen to pop music. I've never listened to a lot of rap.
In general, I think that every genre can have hits that will appeal to listeners of other genres. But I've found my niche, my group of genres that I listen to constantly. Neither rap nor pop is included in that. Why? ... Tomorrow. I'm going to sleep now.)