I’ll offer up a slightly different take.
olegd, Is this your first year doing this? It seems to me that as a relative beginner, you’re better off with more street-focused tires.
I used up the Goodyear F1’s that came on my car and am just about done with a set of Michelin Pilot Super Sports. My next set will probably be the Pilot Sport 4S that’s replaced the Super Sports.
Sure, they’re not going to be as sticky as the track focused tires, but it seems to me that this is better for learning.
Now, I’ve got no experience with anything like Cup2’s or R888R’s but I’ve been told that street tires will give up grip in a more predictable manner and, obviously, at lower speeds which is great for when you’re learning to get the most out of them.
Once you feel like it’s the tires that are holding you back rather than your driving and you want more, by all means move up to a track-focused tire. It’s not as if you’re stuck with the street tire for years. If you keep at this somewhat regularly, you’ll use them up in under 2 years and can then decide whether to stick with them again or move to something with more grip.