I'm not familiar with that machine, but you might ask in the Vintage Machine Enthusiasts forum on this site to see if anyone knows of a third-party walking/even-feed foot for your New Home model. I know there are third party walking feet for many of the vintage Singers, so perhaps something is available that would work for you.
It is a very lovely flimsy. I personally love 100% cotton batting. If you can get a walking foot, my favorite batting is Warm & Plush. If not, perhaps one of the low-loft cotton batts by Quilter's Dream might be a better option. Or you could go with Warm & Natural as long as you quilt fairly far apart (quilting more than 2" apart can cause the stitches to pop in the wash/with regular stress from handling so I would probably quilt every seam). Start in the middle & work your way out in each direction on the center lines; then, you can go back & fill in each quadrant, working from the middle out.
Can't wait to see your finished quilt!