Interesting time to upgrade, but as of right now Nvidia is not the path you want to go down if you are willing to compromise graphical performance.
It looks like you could do with a CPU upgrade- I'd recommend an FX 8300 (120 USD) or FX 8350 (160 USD), seeing as how you wouldn't need a new MOBO with those, most likely. If you wanted to go team blue, the i5 6400 is like 170-190 USD, but you'd need a new compatible motherboard with that, and possibly another copy of Windows (Which I assume you're using) if you don't have a full retail version. However, I'm not sure exactly how low-powered the 4300 is, so this need might not be too immediate, if you really don't want to pay for it.
EDIT: Turns out most AMD cpus sort of level out when it comes to gaming; the major benefit you'd get from a CPU upgrade would be better multitasking/video editing and multi-core heavy tasks.
As for a GPU- don't go NVidia if you are on a budget. Their new line currently is aimed at enthusiasts (And they are absolute overkill for 1080p graphics), with prices starting a 380$, and seeing as how you seem to be alright with compromising graphics, you could probably spend that money elsewhere. I wouldn't recommend buying an 900 series card, unless you get it used. (You could probably snag a 960 which can run the Witcher 3 1080p at like 35-40 FPS for around 140$-150$, if you get it used). They've yet to announce a 1060 or 1050, which are there more midline cards.
If you want a new GPU, I'd recommend waiting until the RX 480 is released in early July, they retail for about 200$, and should be at least as powerful as an NVidia 970 (They claim it to be more, but we haven't seen any independent benchmarks as of yet) ABSOLUTELY DO NOT buy a new Nvidia 900 series card right now. You would just be throwing your money away when better options are on the horizon.
As for the Vram part- you likely won't need 4gb if you get a used card, especially if you don't crank the settings to maximum. I've not played the evil within, but my 960 only has 2gb of vram, and I've never had any problems going in that direction. The RX480 has 4gb of ram on the 200$ edition, and all the new Nvidia cards have at least 8 I think. TEW looks like it only requires 1gb of Vram, as well, but it recommends 4.
It looks like you could use some better RAM, as yours is pretty low speed. You can get an 8gb DDR3-1600mhz kit for like 35-45$.
On top of all of this, you may need a higher watt power supply, but I don't know for sure. AMD's higher-order processors are power-hogs (Much like their recent GPUs predating the 400-series), but I don't know what wattage PSU you have, so I can't say for sure.
So, for a quick breakdown of recommendations
FX 8300 (120$)
RX 480 (200$) OR Used NVidia 960 (140$)
RAM (40$)
PSU* (~50$ for a trustable one)
*Again, I'm not entirely sure you'd need one.