MsMod will be the expert, but I recall something like what you are mentioning- known as a hand tie quilt. One could use battling for the fill or and old/ new blanket.
The top piece is basic squares either hand sewn or machine together/ the backing was a plain sheet of material or bed sheet. One the layers where sewn together you simply used yarn and needle and at each meeting corner made a tie/ bow. Some preferred doing it in the middle of the square.
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These were very popular quilts, usually of suit fabrics, feed sacks, pillow ticking, old cotton dresses and polyesters, tied with yarn, string or embroidery thread and yes, like spidey said, the inside was usually old sheets or blankets. Our foremothers (and maybe some quilting forefathers) used what they had. Nothing went to waste. If you want it to be authentic like that, those would be your ingredients. They wear well and last a long time, but like Marsha said, I would definitely use modern materials to make the job easier. Tying through old sheets is very hard. I've made a traditional quilt like this and it is tedious work. And I own 3 from my grandmother's sister's who sat around and helped each other make these blankets for gifts they would hand out.
In the old days, these would be designated blankets as they were tied. And quilts were only quilts if it was all hand done with the fancy stitching on the top, hand done. No machine involvement at all. As if!!! Of course, this snobbery is out the window and they are all quilts today.
Go pretty cottons, and if you can, I'd use the charm packs like Marsha said. They are pre cut and quality fabrics. Here is a chart:
Use a quality thread to make it last. Cheap thread will fray and wear quickly and the time you spent putting this together will be wasted. You want this to last.
You can go cheap with batting, but I would also try to buy quality. The finished product is only as long lasting as the products you use. Cheaper can still be cute, but it won't last long and won't wash as well. Or, maybe it will last just long enough. It depends on your wallet and what you hope to accomplish. No matter what though, a quilt is a wonderful thing!
Also, as a rule of thumb, tying should be a hand width's distance from each. Use a square knot or surgeon's knot.
As Marsha said, Missouri Star is a great source of easy information. Fons and Porter also have some good youtubes. As do various other quilters. there is always a quilting answer in a youtube!