Your best bet is to shoot for one with an AMD Ryzen chip, as they have by-far the best iGPU available.
Getting a dedicated GPU into a mini PC is a pretty big ask, but the above will even do moderate gaming tasks. My laptop with a Ryzen iGPU plays Guild Wars 2 just fine, for example.
A self-built Mini-ITX box might also be up your alley, as those can take proper PCI-E graphics cards.