The best card that is natively and fully supported in a Mac Pro 1.1 or 2,1 is the Radeon HD 5870. You can find reference design PC cards for sale online for about $30. You can flash the card yourself with a Mac EFI rom for boot screen.
The EFI rom is ATI cards is in EFI byte code. It works as well with 32-bit and 64-bit EFI. The Mac version of the Radeon HD 7950 / HD 7970 / R9 280X should also work on 32-bit Macs like the Mac Pro 1,1, but it requires as a minimum Mac OS 10.8.3, which is not natively supported on a Mac Pro 1,1.
If you run Mac OS 10.10 Yosemite or Mac OS 10.11 El Capitan you can also use a Radeon R9 390X. Radeon Fury X, RX 480, and RX Vega all require macOS 10.12 Sierra, which cannot run on a Mac Pro 1,1 because the CPUs lack the SSE 4.1 instruction set.
With Nvidia cards you should be able to use any card that has web drivers for El Capitan. I believe this includes the GTX 980 Ti and GTX Titan X. Flashed Nvidia cards however require a 64-bit EFI and will not provide a boot screen and will show no video unless the web drivers are installed.