Make sure you measure, cut and then sew borders on, this helps prevent wavy sides.
Press your quilt top well.
Make sure your backing is 8" longer and 8" wider than your quilt top. Square up your backing, this helps lessen the likelihood for tucks and problems on the back.
If your quilt or back has a definite top, mark it with painter's tape or safety pin a note on.
If your quilt has lots of seams on the edges, consider a "victory lap", stitch about 1/8" all the way around the quilt.
Absolutely! Minky is amazing, and looks so great when longarm quilted.
The only limitation is the width of minky. Regular minky is 58" wide, so your quilt will need to be a max of 50" wide. If it is bigger, you'll need to buy Wide minky, which is 88" wide. With wide minky, your quilt can be 80" wide.