When I turned my computer into a Hackintosh about 2 years ago I was using an NVIDIA GTX 660 as my GPU and it worked without any additional drivers because of built-in support in Sierra. When I later bought a 4K display I could not make the GTX 660 drive the display at 4K@60Hz in macOS, although it worked well in Windows.
NVIDIA web drivers
I decided I needed a more powerful GPU anyway to play games on the new display in Windows so I bought a GTX 1060. It worked in Sierra and High Sierra thanks to the so called web drivers; GPU drivers provided my NVIDIA on their website. Without the web drivers you get no hardware acceleration, no 4K as maximum resolution, just one display working … the whole setup is basically unusable.
Those web drivers are version specific, every time the macOS build number changes after some update you need new ones (or to use a script to patch the previous ones). This is a bit annoying, you typically have to wait a few days after every macOS update for new drivers to become available and update then.
No web drivers for Mojave
When a new major version of macOS comes out, like Mojave, you cannot use web drivers for the previous version. NVIDIA needs to release new drivers and they now cannot do it without cooperation from Apple. Citing from the NVIDIA Developer forums
Developers using Macs with NVIDIA graphics cards are reporting that after upgrading from 10.13 to 10.14 (Mojave) they are experiencing rendering regressions and slow performance. Apple fully controls drivers for Mac OS. Unfortunately, NVIDIA currently cannot release a driver unless it is approved by Apple.
Apple basically blocks NVIDIA from releasing web drivers for Mojave, that is the reason the drivers are not out even now half, a year after Mojave release. If you are for example an iOS developer, XCode 10.2, the next version of Xcode, will only run on Mojave and you will not be able to use it unless you upgrade.
AMD GPUs in Mojave
Mojave natively supports some GPUs from AMD. You can buy a RX 560, RX 570, RX 580, Vega 56 or Vega 64 and it should work out of the box, no extra drivers needed. You not even have to install Lilu or Whatevergreen.
Switching to RX 570
I am not a fan of AMD GPUs to be honest but I decided to buy a RX 570 to be able to run Mojave in expectation of Xcode 10.2. The RX 570 (8 GB variant) seemed like the closets match to my GTX 1060 (6 GB variant) and was is quite cheap, you can get it under 200€. But it consumes more power and runs hotter.
I switched the GPUs, booted High Sierra and the RX 570 just worked. No extra settings needed. I did not even need to uninstall the web drivers in advance. I did it after booting with the RX 570.
Update to Mojave
I did a full disk backup with CloneZilla and updated to Mojave. The update went fine, no problems during the process.
The only thing that did not work right a way was sound. The Clover ALC script I used in High Sierra to get my ALC887 working is no longer supported in Mojave.
To get your sound working in Mojave you now have to use AppleALC, which is a Lilu plugin and supports a lot of sound card codecs. My ALC887 is directly supported so I just installed the kext using Kext Utility without any modifications and the sound started working after restart, both playback and recording, using my gaming headset.
Mojave disabled subpixel antialiasing, so if you use a low resolution display, like FullHD, all the fonts look terrible. I run and old FullHD display next to a 4K display and it was really visible. Running
defaults write -g CGFontRenderingFontSmoothingDisabled -bool NO and rebooting macOS made it better but it still feels off.
RX 570 in Windows 10
The AMD drivers are notoriously bad, especially for gaming when you will get a few more FPS in some game but a huge FPS drop in others.
You will also encounter additional problems. When Windows 10 is booting, both my displays show the Windows logo. After the boot is complete, the second display connected via DVI just turns off and it is not even detected by Windows 10. There are many users on the AMD forums and Reddit complaining about this issue but with no solution.
Using a DisplayPort to DVI dongle hepled, but the GPU has a DVI port so it should work directly. Especially when it works in macOS and before Windows 10 is booted, meaning it is a driver issue.
Or when I keep my VR headset connected to HDMI when I sleep the computer, does not matter if it is booted to Windows 10 or Mojave, both displays are black when I wake it up and only a restart helps.
I never had such problems with any NVIDIA GPU.
The AMD GPUs are good enough for driving your (4K) displays in macOS, you basically have no other choice when you need to run Mojave. They work out of the box, no extra steps needed.
If you dual boot to Windows on your Hackintosh, the experience there will not be ideal, quite worse than using a NVIDIA GPU.