I press the fabric first so I don't have the crease any longer. Then I fold the fabric with the selvages together but I keep the sides from touching at first so I can check that it hangs straight. (You can tell when it doesn't because either side will pull. It almost looks like a huge hammock.) Then I let the fabric touch and smooth it out on my cutting surface and square off one side.
I generally cut a multiplied value of my strip width. Example: @2.5" I would probably cut 20" at a time, and then cut that into 8 2.5" strips.
Happy cutting.