MSI 7850 2GB: http://www.overclockers.co.uk/showproduct.php?prodid=GX-191-MS&groupid=701&catid=56&subcat=411

It would be pretty hilarious to run a 3DMark now because there's currently no graphics card in the system (the old one is faulty, hence my hurry to upgrade).

How would I go about uninstalling the drivers? Is it through Device Manager? And should I download the AMD ones before I plug in the card, rather than using whatever is on the disc?

Yes download AMD's latest drivers, you can do that after you plug the card in though.
You can use Driver Sweeper to remove nVidia's drivers. (Or just use CCleaner like I do, uninstall - Then do a registry fix.)

Here's the 3DMark: http://www.3dmark.com/3dm/1311264?

Worse than it should be or about right? It seems kind of low (barely outperforming a gaming laptop, though I suppose the 7970M is supposed to be more or less equivalent to a 7850 anyway).

well i guess its performing as expected, just your cpu is the bottleneck of the system.

you even got the 'Brawn' achievment oO
Your GPU is ready to rumble, but your CPU doesn't want to play.

http://www.3dmark.com/3dm/1311699 is mine with the 7870, but with an intel cpu ...

so according to 3dmark mine is a medium rated pc ... costs betwen ps4 and xbone (~450€)
maybe i should have invested that money in a next gen console instead -_-

edit:
gpu wise the results are pretty close to mine (expected for the difference between 7850 and 7870)
but cpu wise mine has more than double the performance than your amd ...

You also have twice as much RAM at the moment (hopefully my new RAM will come tomorrow).

Where are you seeing the achievements?

ram wont do anything for speed, just loading time. (at best)

under your 'fire strike' > show result details > under the version/date/id

I don't intend to upgrade the CPU for a while, but when I do, how does this look to you guys?

I've checked that it's compatible with the motherboard.

you don't really need to upgrade your cpu i guess for a while.
3d mark is a synthetic benchmark and doesn't reflect real world performance ...

you won't lose that much fps because of your cpu (i guess) at least for intel if you have an i-core (5or7, gen doesnt matter).
but when time comes where you can't keep 30fps on your 1080p games and details already at lower medium it might be time to upgrade.
but most likely an upgrade for a better gpu would bring more fps for the same money ...

cpu would boost maybe from 90>110fps or 25>30fps at best, but a gpu can double your fps ...
for gaming that is. but if you want to stream on twitch, encode videos, cad, compiling, photoshop or other cpu intensive tasks then its time...

hell i would even go that far and claim that your cpu is not slower than what the ps4/xbone have to offer ...

Considering the rest of your system, that score is actually good.
3D Mark also responds well to really tight timings on Ram and if you had a better CPU and tight memory timings with a beastly GPU overclock you should hit around 6k at the most.
Being an MSI card, you have the option to overvolt and overclock the card like no tomorrow later down the road when the need arises.

The FX 8320 is also a great CPU, easily my favored CPU in AMD's line-up currently for it's Price/Performance ratio, they overclock like champs too! Would be worth the upgrade IMHO.

Intel really do dominate the top end, though. Everyone at the top of the leaderboard is running an i7.