For the fake markets in Beijing I would recommend going shopping for the experience alone (it can be quite fun the first few times), but not to actually buy the stuff. Usually pretty bad quality and the markets aren't what they used to be years ago. Nowadays, the fake markets are located in shopping buildings, what the hell. Prices have also gown up. As for the price, as a rule of thumb aim for 25% of the initial quote or less. For reference: long arm shirts are 40-60 Yuan depending on the location, polo shirts a bit less.
For other shopping, I would recommend buying some tea while also trying it at the store. There's a very nice tea street but I forgot the address, I'm sure you can check with local people.
If you like modern art, Beijing has a few artist villages with galleries and ateliers to the north east of the town. 798 district is the most famous one. It was very good 2-3 years ago. Today, you have to know where you're going because some rip-off galleries moved there, too. You can sometimes get
very very high quality art for as little as $500. While not the most innovative, Chinese artists usually are perfect in technique and sometimes the ideas are very good as well. I bought 3 pieces of art some years for around $2000 from an artists directly in his atelier and the same artist's recent bulk of paintings have sold for over $5000 the piece during a vernissage. Not meant as investment advice, just that are hidden gems to be had if you have the time to look for them.
Also, getting tailored suits in China can be a nice thing to do. Bring you favourite suit and give it to a tailor to make a copy of it using whatever fabric he has available. Cost should be under $100, usually less. I had two Boss suits copied and the result wasn't too bad. Or get a tailored cashmere coat for a moderate price but make sure it's really cashmere.
I wouldn't recommend buying expensive luxury articles in Beijing or China in general. Either more expensive than in the US/Europe or fake/damaged/etc.
If you just want to experience big shopping, go to Wang Fu Jin, lots of shops, lots of people.
And you can never steer wrong with the Economist city guides:
This one's for shopping in Beijing. Also check out the Shanghai guide from the same website. The recommendations there are what their own correspondents like and use.
Last but not least, if it's your first time in Beijing, please don't spend too much time on shopping.