To the best of my knowledge, no, you cannot mix & match Nvidia and AMD on the same motherboard, or in the same rig. You cannot have drivers for both at the same time.
If you’re building from scratch and buying parts, you do have to stick with one manufacturer for your build. There are some red vs green nonsense that develops over the years, but it’s like bickering about coke vs pepsi. Honestly, the first thing I look at with GPU’s these days is power effeciency.
Hit up a mining calculator and see if (for example) a 1660Ti at 75watts will give you enough H/s compared to a more expensive GPU that gives only 10 H/s more but runs at 135watts. For me personally, I found AMD drivers more of a challenge and ended up returning my first AMD card for a 1660Ti. But that’s me. ETH miners are right to seek out AMD cards cuz they are great on ETH.
So maybe ask yourself “what coins” interest you? If ETH is on your list it’s mandatory you get at least a 6GB GPU, 8GB GPU’s are better for the next couple of years.
So look at your GPU search with this formula: power efficiency+VRAM size+algorith+Your budget. Then see what looks right to you. If you want to start with a “last generation” GPU you can find them for $50 - $90 used. For current stuff I’d say a GTX 1660Ti/Super at least.