Hi Julia - welcome to a new obsession. The "stuff" in between the layers is called batting. There are many, many choices, but for a beginner, I'd try Hobbs Heirloom (on sale right now at Connecting Threads!). It's not too heavy, quilts well without popping up through the weave (called "bearding") and washes beautifully.
Best tip: do some practice sewing quarter inch seams. Cut two, 2 1/4" square pieces. Layer right sides together and sew the seam. Press the seam to one side. Now measure the joined pieces. They should measure exactly four inches. If not, cut another two, layer and sew again, adjusting your seam width in the direction you need (more than 4", make a slightly wider seam, less than 4", a slightly narrower seam). Iron and measure again. Do as many times as needed to get that 4" width. When you finally have one sewn perfect, mark the bed of your sewing machine with masking tape, so you can repeat that perfect seam every time.
Hi Julia, I agree with Quiltbabe this is a fun obsession. Being a self taught quilter my best advice is to start simple. Try a log cabin or nine patch. My mistake was trying to start with a lone star quilt. Epic mistake. I never did finish that quilt. Good luck and have fun!