Questions on upgrading GPU in refurbished PCs

I'm new to building PCs and looking to make a machine for thermal fluid simulation work, and maybe some light gaming. I've got a tight budget and was wondering about the possibility of adding a graphics card to a refurbished business PC or something similar (Can find Ryzen 5-7, 32gb, 1TB SSD, integrated graphics computers for less than $300).

I know it will need a x16 PCIe slot on the motherboard, and will need appropriate power, but I'm unsure how to go about determining compatibility, as most eBay listings don't have that information.

Is this something that is realistic? Anyone know of people doing this sort of thing successfully? Thanks!