I'd say the graphics card will definitely need some upgrading, maybe a 1050ti or a 1060 (with at least 2GB of VRAM, I recommend 4). Also the power supply. It should be good but if you want more performance, then you will want at least a 400W one. This will then come very close to my own personal gaming PC, which is now broken but i wont go into that, which used an AMD ryzen 5 CPU, a 1050ti and a 400W power supply. That system used to run most major games at 60 fps or higher. Also consider adding more fans as both the graphics card and psu upgrades will increase heat by a reasonable amount. Replacing one of the HDDs with a small (maybe a 64 or 128GB) SSD to run the operating system on (i recommend using windows 10, if it is not already installed, to get maximum compatibility) and keep the other HDD for general storage. Since the PC is from 2013, you may also need to upgrade your RAM to DDR4 RAM for compatibility with other components, look into this and if you need to do it you will also need to replace the motherboard as DDR4 RAM will only fit in a DDR4 slot.
Summary:
Upgrades:
Definitely a better GPU, most likely a 1050ti (with at least 2GB of VRAM, I recommend 4)
Higher wattage PSU, not required but probably a good idea for better performance of your GPU and CPU
Possibly a small (64 or 128 GB) SSD to install your operating system on, keeping the HDDs for general storage
Possible Issues:
Some of these upgrades may require DDR4 RAM (I am assuming that since the PC is from 2013 it is using DDR3, or even DDR2, depending on the budget it was originally built on, look into this and if a RAM change is required, you will also need a new motherboard as DDR4 RAM will only fit in a DDR4 slot.
The upgraded power supply and GPU may also create an increased amount of heat which means you will
need more fans
I also recommend using windows 10, if it is not already installed, for maximum game compatibility.