In the beginning most new sewists choose a universal needle. The point on a universal needle is something between a regular and ball point offering decent stitch quality under a wide range of sewing conditions.
There are better options, however.
The range of sewing needle choices beyond universal is boggling at first: there are sharps, ball point, twin, jeans, stretch, wing, leather, and more.
Skipped stitches on fabric with Lycra content was what prompted my first exploration into choosing different needle styles.
It is a common misconception that you should choose your needle size based on your fabric. In reality, you should choose your needle size based on thread thickness. The thread must fit in the front groove of the needle; when checked it should not be too loose (which causes skipped stitches) or so tight the thread sticks out, causing the needle to get stuck in the fabric as it withdraws.
Just because the thread fits through the eye does not mean it will fit the groove. Refer the the needle diagram at the left. Since you choose the thread thickness based on your fabric -- thick for jeans, thin for dress shirts, etc. -- your needle will correspond to your thread and will somewhat match your fabric. However if you were to sew heavy denim with an all purpose thread, then a 75/11 could work just fine. A thinner needle actually penetrates thick materials easier due to its sharper point and thinner shaft.
Needles are marked with two sizes, European and American. The larger European number refers to the needle's diameter, and the smaller number (after the slash) refers to it's American equivalent. The American number is an indicator of needle size but does not actually reflect any true measurement.
When you're new to sewing, there are so many techniques and skills you're building that choosing the right needle seems less important. There will come a point on your quest for perfect stitches, however, when all the other variables in stitch quality have been fine tuned: you can no longer make any adjustments to your machine, use any better thread, or improve your technique. The only variable will be your needle.
You will now be able to explore how different needle styles affect stitch quality.
I order my needles from a professional dry cleaning catalog (www.cleanerssupply.com). I choose Organ needles, an excellent brand available at a reasonable price. Organ needles are available only in sharps (regular) and ball point because professionals generally use one or the other. If I'm sewing something with Lycra Spandex then I choose a ball point; for everything else I use a sharp.
Schmetz is a brand that caters to the home sewist and offers some additional (and welcome) choices. They have a sharp that goes down to a 60/8, which is an extremely delicate needle good for tiny stitches with fine thread. I also have a Schmetz universal 120/19 that has been working better for me then the 110/18 jeans needle. I also just discovered an Organ 125/20 sharp that should allow me to use extremely thick thread more easily.
I'd like to stress how important it is to change your needle frequently. If you take a new sharp and a ball point of the same size, I'll bet you cannot tell which it is which just by feeling the point. Damage and wear to the needle point is microscopic. As you sew, the needle point will penetrate the fabric thousands of times, wearing down the point and affecting the way the needle sews. If the needle point at any time lightly hits your needle plate or presser foot, it's ruined. As it is difficult to judge actual sewing time on a specific needle, one, or at most two projects, depending on your stitch length and fabric, is a good measure of needle's (ideal) lifespan.
Don't be penny-wise, pound-foolish: change your needles frequently!