Using the correct tools always makes the job easier and usually ends with better results. The biggest problem most of us have with needles is not changing them often enough. Damaged and worn needles will cause problems like broken stitches, puckering, or damage to the fabric to name just a few. The type of needle is determined by the fabric, while the size is determined by the thread you plan to use. We will cover thread another day.
The first number is a European number, the second American. The larger the number, the larger the needle. This is true only for sewing machine needles. Hand sewing needles are just the opposite. Use the smallest number that will pierce the fabric easily. A needle that is too large will leave a hole. A universal needle has a slightly rounded point that works for both woven fabrics and many knits. I often use a universal size 12 with all-purpose thread for general sewing. A ballpoint needle has a rounded point to prevent splitting fibers on knits or stretch fabrics. It could damage tightly woven fabrics.
• A Microtex or sharp needle is good for tightly woven fabrics. Works well on micro-fibers and polyesters with high thread counts.
• A denim needle has a sharp point with a stiffened blade, and would work well for quilting, too. The quilting needle has a sharp point and a tapered tip for sewing through many layers, which also requires frequent replacement.
• In addition to needles with coatings and special materials that handle iron-on adhesives and various glues, there are special needles for embroidery and top stitching.
You can find many good resources online by needle manufacturers that can answer more specific questions, along with wonderful diagrams of the parts of a needle.