First of all...congratulations!
It all depends on if you are wanting to maintain the integrety of the original quilt and whether you are wanting to keep them as heirlooms to pass down through your family or are going to actually use them for everyday. Sorry, I cringe at the thought of using them since everyday use and just dust alone will destroy a quilt.
Keep in mind that having to pay someone to machine quilt your quilts could run you around $200.00 for each quilt. That's the going rate for machine quilting here for a queen size quilt.
I also have a quilt made by my grandmother and another set of just blocks in which the fabrics used are over 200 years old made by my other grandmother and great aunt.
The Quilting Appraiser that viewed them said to retian their value to either leave them as they are or to complete them using the same methods. She also suggested that I use high quality muslin for the backing and only use high quality cotton batting. She insisted on hand quilting only. My Mom gave each of us girls a few of these blocks along with pictures of my grandmother and great aunt that made them and we are all going to frame them for wall hangings. They have to be framed like a museum would frame their artifacts and kept out of direct sunlight or they will deteriorate. Mine are still in my cedar chest wraped in a white sheet because I can't afford the muslin, batting, and expensive frameing right now but they are on my list of important projects to complete.
You can use the newer fabric for the backing. Just wash it first. Also use cotton batting. The hand quilting can be as simple as quilting in the ditch or 1/4" around the outside edges of all seams. This method will cut down on your sewing and still hold the quilt together. It's how I started out and it was easy. Your stitches do not have to be perfect or concise 10 to 12 stitches per inch. I've seen lovely quilting done with only 6 to 7 stitches per inch.
Never, ever, wash your quilts in a washing machine. It will bunch of the batting and can cause tears and wearing to the quilt. If you must wash them, lightly soak it in your bathtub, press out the water, do not ring it out, then lay flat on a white sheet to dry. Preferably somewhere like a covered porch outside. If your quilt has any dark colors, be very careful because the older fabric colors may fade into the lighter colors.
Don't fret about keeping the quilts as 'works in progress'. I just saw a quilt this week that was completed by 5 generations of the same family and it is a treasure! Maybe one or more of your grandchildren or even greatgrandchildren will enjoy adding their hand to completing one of these quilts.
Good luck with your quilts and if you have any questions, feel free to ask.