Information for stringing racquets:

You may go to Paragon (867 Broadway, around 18^th Street) to string your racquet.

The most popular choice of string is probably Yonex BG-65. Cost of the string including stringing service is $15. When you string your racquet, you can choose the tension of your string. Different players have different preferences on tension, and here is the general advice: if the tension of your string is high, your smash will be more powerful, but your have to replace your string more often. String tension of club racquets is around 18lbs, and string tension of national level players is typically over 30lbs. You need to leave your racquet in Paragon for around 2-6 days, depending on the availability of the stringing machines.

Information for purchasing racquets:

If you live in the US:
Since most sports equipment shops in Manhattan only have very limited choices of badminton racquets, it is more sensible to buy club racquets online. You can browse the websites of different badminton racquets manufacturers e.g. yonex.com to choose your racquet. However, Yonex does not list all of its products online. Once you are done, you can type your racquet model on google. You may find deals in ebay, amazon.com etc.

If you live in Asia:

Unless you want to get a new racquet asap, you should buy a racquet in your home country and ask your friend to send the racquet to you. There are three reasons for doing this: firstly, you will have more choices; secondly, you can string your racquet and purchase grips at lower prices, thirdly, the racquets in your home countries should be at least 30% cheaper. A rough estimate is that if you plan to buy a racquet that is over US$70, you should buy it in your home country.