There’s 2 types of SSDs that you should be concerned with, SATA and M.2 NVME. Sata are usually black connectors in usually the bottom right of a motherboard, same type of connector a hard drive would use. You can get SATA SSDs for fairly cheap, I’ve got 2 2tb ones in my computer, but they’ll be much slower than an M.2. Still much faster than a hard drive though. M.2 NVME is what I assume the 500 GB SSD is?, usually located around the graphics card slot, there should be a line of screw holes for different sizes, and a connector at the end that you slide the m.2 into.
If you ever need help, there are plenty of references online if you search how to install a M.2 SSD or a SATA SSD, and once it’s installed, tutorials on how to format it do you can use it.
Godspeed, hope things get better for you