Hello, Charlotte:
Well, I did some research, too, and here are my thoughts:
1. OLED is superior to any other display technology currently available in terms of screen quality and speed. It is also fairly new, and I haven't been able to find any long-term tests or reviews. There are lots of people worried about burn-in, but no-one has yet stepped forward and actually provided an answer based on personal experience, i.e. ownership.
2. You may have come across these web sites yourself, but I'm going to link them anyway:
https
/www.pcworld.com/article/3083401/hardware/the-momentum-for-oled-laptops-and-tablet-pcs-has-faded.html
This article offers some business details about OLED laptops, but it's more than a-year-and-a-half old so my guess is that the industry has either rectified the 'burn-in' issues since then, or decided to kill OLED development altogether.
https

/www.kitguru.net/lifestyle/mobile/laptops/leo-waldock/alienware-13-r3-amazing-oled-screen-with-qhd-resolution/
This KG article is from July this year, but it's a traditional review so there are no details about burn-in. Instead, the reviewers are quite over the moon about the OLED panel and rather less so about the Alienware itself.
Finally, there's this article from September this year:
https
/www.windowscentral.com/oled-laptop-displays
Here you learn that (a) burn-in is still a concern, but less so today, (b) some manufacturers are still pushing OLED laptops, so the technology isn't completely dead, and (c) steps are apparently being made to minimize burn-in, but it's always going to be there.
3. From your personal details, I have to say that $2,000 is rather a hefty price for a laptop screen, even if it's the best one available. As a student, you may appreciate the screen in more everyday situations than you would a TN panel, but unless you're majoring in photography or graphical design, I think you'd be better off with a decent and much less expensive IPS panel.
4. As for gaming, your budget will get you a host of powerful 6GB or 8GB 1070-based gaming rigs, most of them with more RAM and some of them with an IPS panel. They're designed to run at 1080p, and so are most of the sophisticated AAA titles you'll come across.
Cheers,
GreyCatz.