hi camellia tree!
last Christmas I chose plain brown kraft paper in a huge roll from the post office and bought beautiful wide ribbons. Everything looked magazine-perfect under the tree, and as there was tons of colour and pattern with the ribbon, the brown paper was a grounding rustic counterpoint to gorgeous, swank, (re-usable) ribbon. White banqueting paper would also serve the purpose admirably, and gives a different feel to the base. Wired ribbon can be ironed and reused.
also, I love Christmas and so all of my edited Christmas decorations which survive to the next year are boxed in Christmas-themed boxes, which, when empty of ornaments (now on the tree or around the house), hold new gifts tied in plain ribbon.
alternatively, for gifts that leave the house, I use gift boxes and bags only, and re-gift the ones we get. I always have a few extra wine bags as there are always invitations at that time of year, and it is easy to pop out and get a good bottle of wine but finding an elegant gift bag? usually means another trip to another shop. I keep all paper and ribbon in an Ikea under-bed system.
btw I love the idea of a shiny red roll but I have never come across that either. hope you find it one day!
as for your scraps, if they are smaller than 24" square they are too small to wrap pretty much any box. use them under the cat food dish and toss them weekly when you clean, or use them to line a drawer, or simply drop them into a paper recycling bin. Only keep the best, and only one or two of the best.
I am a recycler of wrapping paper, or was, until I realized my system was way more sexy...
