Never ever use the lines on your mat for quilting. Just don't do it. Not so much from accuracy, but because it will seriously decrease the use/lifetime of the board. You will over use portions and not use others, and you will make lines that eventually will lead to skipped threads.
When I start with a new quilter, I turn over the mat to the unmarked side and teach them how to cut correctly using rulers, that plus the need for a reliable seam allowance are the two biggest starting points for sewing.
Be aware as well that different rulers are designed slightly differently, whether you cut on the line or next to the line. For most of this, it doesn't matter much but yes -- read the directions that come with your rulers.
And change your blades often! If you are pressing down so hard your shoulder is sore, you should have done it a few months ago!
I need to change mine, it was getting dull and then I just ran over a hidden pin and it's time to go. Our fabric and time are more valuable, but them on sale -- like when I get stuff from Amazon I check on the current price and whether I should order a few more or not.