Answer: Your plan is pretty much on target! Digging up the grass completely will insure it will not resprout. (Be sure to put the grass on your compost pile--what a bonus!) If you were to use thick black plastic sheeting rather than paper, it will kill any dormant weed seeds that are bound to be uncovered, as well as any grass roots that you may have missed. I would never recommend black plastic to be used in a garden bed, because it will deaden the soil that lies under it. But that is exactly what you want in a path.
Furthermore, you may want to consider using gravel rather than mulch for your paths. In a few years organic mulch will decompose to a fine compost, and then you will be fighting weed seeds continuously. Although some seeds may sprout in the gravel, without the soil, most will quickly die.
In a nutshell, for a path I'd dig out the soil, lay thick black plastic, and cover with gravel. You may want to line the edges of the paths with large stones or bricks or some other border to keep the gravel in the path. Nothing beats an inviting path through a garden!
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