noob question regarding GPUs

I'm finally setting up my first mining rig and obviously I'm struggling to find an affordable graphics card, which got me thinking about doing one of two things
– Buy several affordable GPUs that aren't great on their own, but profit if I get several (for example each GPU would profit 0.05 but I can buy several at once since the GPUs are cheaper + not as in high demand)
– Have a rig with both AMD and NVIDIA GPUs

This leads to my question; can I have two different brands of GPU on one rig, and if not could I have different types of GPU on one rig (like an RX 570 and RX580)