When you select your wallpaper in Settings you get the option to zoom and position it by pinching and dragging the picture. If you do this in portrait view, what you see will be what you get in portrait mode.
Personally, I keep flipping it back and forth when I'm positioning my wallpaper, so I get a compromise of what looks best in both modes.
Ideally a wallpaper should be 2048 x 2048 for the iPad, though the iPad mini's lower resolution won't show any degradation at 1024 x 1024. Gabriel's recommendation is exactly the iPad Mini's screen resolution in portrait mode. If you use those dimensions it will look fine in portrait, however if you go to landscape the image will be cropped top and bottom with some letter boxing (black space) to the left and right. Unless you zoom in, of course.
Hold in mind that if you zoom the image when setting up (as I mentioned above) the image may not be as crisp. Then again, if you use the larger 2048 x 2048 image, you can do quite a bit of zooming before this happens on an iPad Mini.