There are many opinions on how best to ship the jewelry you make.  I remember looking for hours on the Etsy forums to read how other sellers do it, back when I first started selling online.  Shipping jewelry is actually very easy and hassle free, if you don’t complicate it too much.  The two main factors to consider are cost and appearance.

Cost
Obviously, the more elaborate your packaging is, the more it will cost.  Keep in mind that your packaging will also increase shipping weight and plan accordingly.  If you want to go super inexpensive, use tissue paper and bubble mailers.  This only works if you have jewelry that is not overly fragile.  I ship this way and have for years without any trouble, but chunky or glass jewelry might not fare so well.

Appearance
One thing my own packaging lacks is that special touch.  I don’t feel it really conveys a warm fuzzy feeling, which is important to some jewelry sellers.  I agree that dressing up your jewelry like a little gift will make it seem more special, but do your customers really want to pay for all that fluff?

The bottom line is, you need to pick a method that works for you, without worrying about how others do it.  If you want to use elaborate packaging to make each piece seem like a special gift to your buyers, do it!  Your buyers will probably love it.  If you want to keep costs down and emphasize practicality, go for a more subtle option.