PCI-E is backwards compatible, meaning even if your Motherboard supports gen 4.0, any gen 3.0 GPU will also work on that same board. Also, suppose the board supports Gen 3.0, and GEN 2.0 card will also easily work !
There won't be any performance drop whatsoever (you won't even notice it while gaming).
All PCI Express versions are backward and forward compatible, meaning no matter what version the PCIe card or your motherboard supports, they should work together, at least at a minimum level. One important thing to know, however, is that to get the increased bandwidth (which usually equates to the greatest performance), you'll want to choose the highest PCIe version that your motherboard supports and choose the largest PCIe size that will fit.
For example, a PCIe 3.0 x16 video card will give you the greatest performance, but only if your motherboard also supports PCIe 3.0 and has a free PCIe x16 slot. If your motherboard only supports PCIe 2.0, the card will only work up to that supported speed (e.g., 64 Gbit/s in the x16 slot).
The only slight disadvantage is that it will only have the maximum bandwidth provided by the slot; i.e., if you install an x16 video card in an x4 slot, it will have only x4 bandwidth available.
To reach the maximum performance possible, both the expansion card and the PCI Express controller (available inside the CPU or inside the motherboard chipset, depending on your system) have to be of the same revision. If you have a PCI Express 2.0 video card and install it on a system with a PCI Express 3.0 controller, you will be limited to the PCI Express 2.0 bandwidth. The same video card installed on an old system with a PCI Express 1.0 controller will be limited to the PCI Express 1.0 bandwidth.
But never mind all this theory, just install any GPU on your current MOBO, and enjoy playing Games. There won't be any significant FPS loss. Which PSU do you have ? Rest of the PC specs ?