The "bracket" is called a "derailleur hanger", and often varies from frame model to model. If you can figure out what model and (hopefully) year your bike is, there's a good chance you can get a replacement derailleur hanger pretty cheaply ($10-20).
The rear derailleur itself works to one of two standards. Shimano is the main standard, and some (but not all) SRAM shifters/derailleurs use a different standard. Your derailleur must match the standard used by your shifters on the handlebar. Thus, you need to identify the model number of either the destroyed derailleur or of the shifters.
Here's one possible type of derailleur hanger:
http://cgi.ebay.com/ws/eBayISAPI.dll...m=270435439556
Here's another:
http://www.amazon.com/DiamondBack-32.../dp/B002X03Y1W