???
The real problem in that scenario is your CPU which won't deliver a constant 40+ FPS
Dude, that's called a bottleneck, which is bad. I don't mean to come down on you seeing as most of your advice is solid. But you told him "I'm not sure you really understand what bottlenecking is. If you do, then you wouldn't be asking." and you yourself don't seem to be able to convey it well either.
Precedentbug, the issue/bottleneck is your older CPU. The PhII and FX chips from AMD are now ~10yrs old, and not well suited to current gaming needs. They will bottleneck in current games and bottleneck faster GPUs. I agree that an older midrange or current lower end card is a good upgrade for you. The 950/960, 1050, 460 or maybe the 470. (The 470 gets a bit of a bad rap because it's normally found for $10 less than a 480.) While any card can fit in there and work, because of your CPU bottleneck it's important to not spend too much on it as you won't get the full performance from the GPU.