Great question.
First, my suggestion is to dress up in an outfit that you would like to accessorize with jewelry. Then hit a major department store that has a large jewelry selection. Most major department stores will offer a full range - from relatively inexpensive costume pieces, on up to expensive investment pieces.
Bring a friend if you like feedback. Try on tons of jewelry and see how it goes with the outfit. Experiment. If the store isn't too busy (try going early in the morning), ask a salesclerk for suggestions. You don't need to buy anything - this is all about experimenting and learning what works/doesn't work, what you like, don't like. Once you get a better sense, then you can go online or hit bargain shops.
If you do happen to find one awesome necklace that works well with the outfit you wore while shopping, then take it home and see what else it works with in your closet.
And on future shopping trips, wear it. I have been finding lately that when I wear a particular necklace, I tend to somehow naturally gravitate towards clothing that would work with it.
I do think if you are shopping in a specialty store like BR, AT, ATL etc it is smart idea to look through their accessories to see if anything works with any items you have decided to purchase. I've kicked myself on numerous occasions for not doing this, because later I can't find anything to work quite right.
With a few exceptions in my early career, I only started wearing necklaces fairly recently. Necklaces weren't really my "look" for a long time - mostly because they tend to be too long for my petite frame. But they can be shortened and if you can't be bothered to take them to be shortened, and it's not an expensive piece, you can always tie a knot in the chain to shorten it.
During my non-necklace phase I was much more into earrings and bracelets. I had a long brooch phase in the late 80s/early 90s.... and I am searching all over the house because I tucked them away somewhere for safe-keeping.... now that they are back in style I want to bring them out again!!!
I find jewelry all over the place:
- department stores
- specialty stores
- designer knock-off stores
- arts festivals
- my sister (who makes jewelry as a hobby)
- even places like Claire's.... cheap as can be, usually breaks, but can be an inexpensive, harmless way to give a style a try.
I do not buy online because I absolutely have to try on first - for a petite person scale is absolutely critical.
Department stores are, in my opinion, the best place to start.