AGI i dont know... is it the one in some PCI-X boards (mainly servers, w/c looks like an extended AGP slot)? As for PCI-E 16x and 1x they are multipliers for the slot's speed (in gbs per sec i think).
Typically, graphics cards use PCI Express x16 slots. That's a PCIe slot configured with sixteen individual data lanes. These data lanes are physical connections, and that's why an "x16" slot is so ...