If you're buying ready-made assets then you're probably not interested in having to repaint textures or modify meshes. So unless the asset already comes mostly under the style that you want, the most that you can change is on the textures: downscaling any high-resolution textures so that they're more pixelated, then using image adjustments to make those textures look more uniform: lowering/increasing color contrast, saturation, the level of noise etc.
If the textures are different "morphologically" (hand-painted brushwork vs photographed textures for example) then there's not much to be done unfortunately.
The best approach would be to make original assets of course, precisely within the visual style that you're going for. You would make them yourself or hire one or more artists to make them.