Jetson Nano is designed for edge inferencing. It is not needed for deep learning (it is only for deploying). You still need a CUDA device for training. Just buy a nvidia (gaming) graphics card which fit your budget. Titan V/Titan RTX is fine but too expensive. Better to choose 2x RTX2080Ti. GTX graphics cards (without tensor cores) are also good if you can't afford a RTX2060.
For edge inferencing device like Jetson Nano, there are:
Raspberry Pi, Kirin 970/980, Hisilicon Hi3559a, NextVPU N171, Rockchip RK3399Pro/RK1808, Snapdragon 845/850, etc...
Do NOT buy if your are not familiar with them.
RX480 can be used for deep learning. There is a framework called ROCm. But it is not the first choice.