Welcome from NJ.
I check my fabric folds as Sewnoma mentioned. I also prewash so I MUST refold my fabric. But yes, fold in half - selvage to selvage and check to see how flat the fold is. Wiggle the selvage edges left/right to get the fold flat. If you have a large enough cutting area, you can do this flat on the table as well but you would then start at the folded edge and let the selvage edges fall where they may.
What I do when I am making that first cut to straighten my edge is to cut from the opposite side (selvage edge) for that first cut so I don't have to flip the fabric - especially when I'm dealing with yardage. I have a couple of spring clamps that I can use to hold my ruler in place after lining up on the folded edge. Then I can go back to the 'normal' folded edge side of the table and continue cutting my strips.
Good luck - you'll get there.