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When deciding between a rectangular sticker and a sticker without a background, there are a few aspects you should definitely consider:
If your design is not available as a vector graphic, you should be aware that if your sticker has no background, you will have to vectorize your file first, which may result in additional costs.
If your motif has transparent areas you should note that these will be white on a rectangular sticker and not printed on a transparent foil. However, a vector graphic may not have transparencies either, so you should simply remove these areas so that they can be cut away.
White areas in your motif may not be visible on a rectangular white sticker, as these disappear with the background.