Not sure if I've replied in here already, but here's what I'm thinking today.
The answer depends on what you like to wear. I rarely wear a necklace, so that would be a waste for me.
Focus on classics that you'll wear a lot. I really regret a lot of the novelty pieces I bought in my twenties. And focus on things that would make a good impression if you wore them to a job.
Don't overspend, and don't think you have to buy name brands like Tiffany or Cartier. If you have roommates, don't get diamonds! I see a lot of people recommending diamond tennis bracelets, but in my twenties I can't think of a single time I'd have worn one. Plus there were always odd people wandering in and out of my apartment and spending the night -- real diamonds would have been stolen within a month of my getting them.
Keep all of the jewelry you buy. I have bought/sold/bought/sold basic gold ball studs at least five times! I wish I'd have kept the pair I bought in my twenties, but at some point my hair was long and I wasn't wearing them so I sold them. Now that my hair is short, I'm wearing them again. Ditto for yellow gold versus white gold...I can't imagine going back to yellow gold, but I know it's likely to happen at some point.
All of that long-winded advice aside, here's what I think a woman in her twenties should acquire:
1. Basic everyday studs. Think pearl, gold ball, or a basic shape like knots. If you can afford diamond studs, don't make them too big (over .5 carat would be frowned on in conservative industries like finance, IMO) and make sure you have a way to keep them locked up at home.
2. Basic everyday hoops, 1" or less. Best jewelry advice I ever got was, 'don't wear hoop earrings bigger than a quarter to work.'
3. A watch. Even if you don't usually wear one, you'll need one in job interviews and meetings when you want to be subtle about checking the time. Get something low key and appropriate for the most conservative job you can imagine.
4. Either a ring or a bracelet that can be worn every day. We all like to see our jewelry, and we don't want to look in the mirror all the time, so 'hand candy' is ideal.
5. A subtle necklace that can be worn daily. Something as simple as a chain with a pendant, or a chunky-- but not tacky -- link necklace.
For trendy items, get costume. I'm glad I didn't spend a fortune on chandelier earrings, or funky brooches, when those things were In.