Confusion regarding Mac Pro graphic cards
Which version of macOS runs on your MacPro? I believe 10.11 is the last version that the cMP3,1 supports... Anyways, if you plan on using the Mojave Patcher I would recommend getting a GTX680. If you really can't live without a bootscreen I would recommend looking at flashing tutorials for NVIDIA GPUs. There are a few on YouTube (esp. GTX680) and macrumors is also a good source. You could also buy a flashed card from MacVidCards, but they are a bit pricey..

I don't miss the EFI Screen on my MacPro 5.1 with an unflashed RX580.

Good Luck!