Let me try and clear up a few things that you seemed confused about. The fglrx driver you are currently using is the AMD proprietary graphic driver. If I assume it is the one you installed from the Driver Manager, it just means it is an older version.
I know when I was on Maya, as a complete newbie I didn't know which one to install so I tried the fglrx-updates release and had some pretty bad stability and graphical anomolies in Cinnamon. I *think* I had also tried installing the latest driver off the AMD website and still had the same issues. The only stable driver for me on Maya Cinnamon was either the FOSS, or fglrx driver.
So really, it was the open source AMD driver, or an older AMD proprietary driver that worked for you in this. I don't know how common this is. I've had my AMD HD5770 in my system for I think four years now and have never any sort of weird instability issues. Just make sure that after a fresh install of LinuxMint that it fully updated via the Update Manager in the panel before installing any proprietary graphic drivers.
I am *thinking* about giving the latest AMD driver a go in Mint 17. Is this something that alot of you Linux gamers do, or is it highly advised against doing that?
Yes, you can do this, but currently the only compatible graphic driver with LinxMint 17 that is based upon Ubuntu 14.04, is the 14.6 beta driver on AMD's web site. I've been using the current version and the prior one with no issues. If you look at the release notes you'll see that the 14.4 stable version is not compatible. And my experience of accidentally installing it showed that to be the case by screwing up the system and requiring my to re-install LinuxMint. By installing the 14.6 beta graphic driver you MAY gain some additional games that run properly under WINE. Out of the three old Windows games that I tested on LinuxMint 17 Cinnamon, only one played properly after installing the 14.6 beta driver. The other two would only play correctly in an emulated desktop. I'd like to recommend that if playing games is important to you on LinuxMint, that installing the XFCE version of LinuxMint 17 has much better game compatibility and you should be just fine with the AMD proprietary graphic driver that is installed from the Driver Manager. My testing showed this to be the case, and installing the 14.6 beta didn't improve anything further. There is something about the Cinnamon desktop that is stopping games from running properly. I'll be making a separate post about this later.
In the current fglrx release driver, there is a "Tear Free" setting, and it seems to work okay, but it forces Vsync on, which sometimes is fine, but other times it makes the annimations choppy [depending on the game].
All the modern fglrx/AMD proprietary graphic driver version have this tear free setting that I always enable. It's the only way to get acceptable looking videos and games. It does say that it requires additional graphic resources when enabled, so perhaps this accounts for the choppy animations assuming it is not a WINE issue. I also recommend you set the graphics processor to maintain the aspect ratio in the AMD Catalyst Control Center so that if you have a wide screen monitor your old games don't get automatically stretched to fill the screen. This keeps them looking correctly as most old games are set to run in 4:3 aspect ratio screen resolutions. Where as modern wide screen monitors are either 16:9 or 16:10 aspect ratio.
I also tried removing the ATI drivers and used the FOSS driver as well, but the tearing is still present.
My testing showed the open source AMD graphic drivers to be really prone to screen tearing and not have very good game compatibility. So this is not likely to be a good option for you.
I hope you are able to figure something out that works for you.