PCI basically doesnt exist anymore unless your working with older systems, dont worry about it.
PCI-Express replaced PCI, and is whats standard now. The generation (PCI-e 2.0, PCI-e 3.0) just refers to new revision of it, main difference is the amount of bandwidth.
All your PCI-e slots have a number next to them, either 1x, 2x, 4x, 8x or 16x. That refers to the number of physical lanes/wires between the GPU and CPU which is indicative as bandwidth. Gen 3 has double the bandwidth of Gen 2, so a Gen 2 8x slot is equivalent to a Gen 3 4x slot in terms of bandwith.
As long as your plugging your graphics card into Gen 2 8x level bandwidth, your fine. Graphics cards arent nearly capable of taking advantage of Gen 3, which is more of a...