Iceblossom

Oh my goodness, "Deadly Taffeta" if that isn't a band name, I don't know what is!

Welcome to the boards and the world of quilting.

I would probably finish up the one partial strip somehow and then I like the idea of using the existing bars between bars of either plan fabric, or maybe sets of blocks where you are learning your quilting and doing what you want to do with your types of fabrics. You can mix the old/new and the generations and skills nicely that way.

It all depends on where you live, but here in Seattle (waving from a safe personal space) we have thrift stores filled with everything you can think of, including fabrics. Part of what I like about quilting is the recycling aspect (but I wish I did have the budget and space to buy all the new fabric I like). Especially for finishing off what your mother did, you may be able to find a bag of scraps for very little. We also have Craig's List here, I regularly look for people wanting fabric and often see ads about people wanting quilting scraps.

Edit: In my thrifting I often find UFOs or unfinished tops. Often there is a clear reason one why they didn't get done, others less so. While there are times that I make my work fit in, there are other times when I decide to show where I started and make some changes. Even if it fits in on the top, say if the original quilter used white thread to piece, I would switch to blue to show where my hand went in.