I don’t know what anyone else thinks, but as a Linux newbie it seems to me that you’ll be making life difficult for yourself with that old card.
Ubuntu is hard to beat for hardware compatibility and its ability to set itself up automatically. However, the AMD R9 360 ceased receiving support for proprietary drivers as of Ubuntu 16 and transitioned to using the AMD open-source driver. As noted in the Mint link mentioned above, it was suggested to modify the boot command for it to function properly. If you wish to utilise the current AMD proprietary drivers, you'll need to enable the HWE stack on Ubuntu, which also requires using the command line.
A lot of piddling about that you don't normally need to do with Ubuntu.