I tried installing either mint or ubuntu on my 3 year old desktop with a 3 year old AMD GPU, neither distro could detect and install driver for my AMD GPU. While on my laptop which has integrated Nvidia GPU, mint could correctly detect and install the driver. So is it that AMD GPU not supported in Linux? However I've went to AMD site and saw they have Linux driver for download, which I've tried one that suppose to work with my GPU model and ended up trashing my Linux installation.

1st question, what's the card?

The old open source "radeon" driver wasn't very good with a LOT of chipsets. It was OK at best.
The proprietary "fglrx" drivers (which is probably what you downloaded) had pretty good support, but won't work with newer versions of...xorg? It's something, I don't remember if it's xorg, or a component of xorg.
The new open source "amdgpu" actually works VERY well...if it supports your card and your kernel is new enough to have it.
The new proprietary extensions for the open source driver "amdgpu-pro" work very well from what I've read, but I haven't had a card to try them on in the little time they've been available.

Thank you for your answer.
I think finally I'll just switch to Mac, since I'm tired to fixing stuff, pouring through wikis, forums and what not so I could focus on "get stuff done" instead. And I just hate the spyware and bipolar windows 10 UI, where it just couldn't decide it wants to be a phone/tablet or a PC.

Have a quick look at Manjaro, it's driver detection is pretty good plus it draws from the Arch repos so the drivers are pretty up to date.
If that doesn't work then yes you're gonna have a hard time getting it working I'm afraid. Probably looking down the Catalyst route which is not pleasant

A whole section of "older" cards are only supported by the radeon open source driver now. Otherwise linux supports AMD fairly well. Now having AMD and nVidia proprietary drivers mixed on an install is problematic. And for most of my low end AMD gpu's, the radeon driver is good enough.

The older cards stopped having a functional proprietary driver since kernel 3.4.x. So if you find that old driver, you might need to run that old (or older) of a kernel to use it. But most of those cards are well supported by the radeon open source driver. Just not the current fglrx or crimson ones.

On a side note, the proprietary driver for AMD (ati) swaps out libGL.so, so if you're switching "back" to the open driver, be aware that you'll need to restore that file to the open variant. With dpkg-divert on deb based distros and/or reinstalling the libgl*-mesa-* stuffs that have that file. Check the /var/log/Xorg.0.log or equivalent to verify which lib is used, or check the glxinfo providers.

$ glxinfo | less
...
server glx vendor string: SGI
...
client glx vendor string: Mesa Project and SGI
...

For the open source radeon driver. Also check lsmod to make sure you're not mixing fglrx and radeon drivers. Not normally an issue with a fresh install and most modern distros. But something to check if you've been using the same install on lots of machines, or are otherwise overly paranoid.