How to tell what graphics card will work with my pc?

If you have an open slot that accepts the type of card (usually PCI-e 16X) and you have adequate power and correct connector (on many high level performance cards) and enough open space inside the case, no problem.
If this is a laptop, no card will fit. You are stuck with what you have.

If your machine has an available PCIe slot, then you would want a PCIe card. Your motherboard may be a 1.0, 2.0, or 3.0 version but fortunately all generations of PCIe cards are backwards and forwards compatible with all generations of PCIe slots.

There's either agp or pci an yours is pci. Agp is now outdated so there's only one interface that is on the market.