I am making my daughter a quilt from some vintage fabric I got on Freecycle.

It will save me a LOT of money to make one rather than buy one, and this fabric will be great to make my first one with.
How do I attatch the soft fluffy stuff (what is it called? batting?) to the fabric? Also, is it okay to serge the squares together? Do I do it from the center out? Or, can I serge a strip and then serge that to another strip?
I could really use a basic how to from a pro.
I also am confused of how to do the last part so that it doesn't show where I sew it shut.
Also, how do I do applique without it ravelling if I only have a basic sewing machine?
Thanks