Non-acetone nail polish is plenty effective. It sometimes requires that you scrub a little more than you do for acetone, but it sure smells better and is less toxic. It helps if you let it soak in a little bit before you start trying to remove it with a cotton ball.
Non-acetone nail polish remover works just fine for taking off any color of nail polish. The only time it is recommended that you use an acetone nail polish remover is if you are trying to remove acrylic tips or full nails. The nail polish remover that I find works best is Cutex. Store-brands can sometimes leave your hands feeling dry.