-The type of GPU it's using. Names like RTX 2070 Super, RTX 2070, RX 570, GTX 980ti, etc are representative of the Graphic Processing Unit (GPU). It pays to know how these GPU's stack up against eachother. Some cards like the GTX 1650 don't offer very good performance for the dollar. This is where it's a good idea to read reviews and benchmarks.
-What GPU/Graphics card is needed to run modern games at the settings and screen resolutions you desire. For example, you're pretty much going to max out the settings on any game at 1920x1080 with an RTX 2060 Super while getting +60fps, but you'll max out the setting on most games at 1920x1080 with a GTX 1660ti. With a card like the RX 570, you'd have to adjust the settings to get 60fps. Basically you'll need to consider the monitor you're using or the monitor you plan to buy.
Something like an RTX 2070 Super is overkill for a standard 1080p/ 60hz monitor.
-Your Power supply and the power requirements of the said Graphics card. You might have to upgrade the power supply for some cards. The good news is a 550w power supply will work with most Graphics cards on the market. Nvidia and AMD generally recommend a 650w or 750w power supply for their Top Tier cards like the RTX 2080ti.
Things that might be secondary.
-The amount of VRAM that come on the card. Most cards come with 6gb or 8gb of RAM. Budget cards like the RX 570 or GTX 1650 come with 4gb of VRAM and there is a 4gb variant of the RX 580. The 3gb GTX 1060 should be avoided.
-PCI-E aka PCI-Express reversions. All versions of PCI-E are backwards and forwards compatible with eachother. However, there are cards on the market that need the newer UEFI firmware. If you bought your system within the last 5-6 years, it most likely has the newer UEFI type of Firmware. The older BIOS type of Firmware was widely used until 2012.