It's mostly inworld content that is horribly "optimized", if at all, but well...
You state that you have limited knowledge of computer hardware, but you wish to exchange and upgrade single parts later on. So you wouldn't mind building a machine from scratch? However, with used second-hand components, since that limited budget only allows for such?
Does your old machine still exist? Can some parts (hard drives...) be re-used?
I'd suggest looking for an i5-2500, optionally the i5-2500K which can be easily overclocked for a little performance gain.
Mainboards with a Z-chipset allow overclocking, the other letters won't.
RAM might do at 8 GB if costs really need to be cut down, but then make sure to have more free ram slots for a later upgrade.
Stock cooler or for more silent and efficient cooling a third party tower cooling solution, about $30.
As for graphics, there is a pretty wide choice, especially if you happily ignore the Green vs. Red prejudices...
For used Nvidia GPUs, look for: GTX 760 (lower end). 960, 770, 970 (middle) or good offers for a 980 (ti).
Preferably 4GB VRAM than 2... the GTX 970 coming in at 3.5 GB full speed and 512 MB much more slowly connected RAM. Current generation: GTX 1050 Ti 4GB.
AMD: HD 7850, R7 270 (low end). HD 7950 / R7 280(x) / R9 380 (middle class). ... or perhaps even a current generation RX 470.
Put into a Midi-Desktop case with a front and an outlet fan for proper ventilation.
I'm uncertain about used power supplies. Consider a new one by Corsair, SeaSonic, EVGA, anything but some cheapskirt "1000s watts for 20bucks!!11!" crap that will likely blow up itself and your other hardware.
500w max from a quality brand for that suggested setup which seems to be ~ $ 80, looking at Newegg and Amazon.