For regular desktop use (and graphically lightweight games) you don’t need a dedicated GPU (assuming your CPU has something built-in).
If you want to play games with heavier graphics than you need a dedicated GPU.
Generally speaking: AMD GPUs are preferred, since Nvidia GPUs are harder to get working due to extra drivers. Though I’ve heard it’s definitely possible.
Edit: second hand is usually fine, but watch out for stuff that’s been used for cryptocurrency mining; those have been worn down a lot more.
So basically The Man in the High Castle, right?