If you intend to keep your Verizon service a "quad band" phone will be more than overkill. Brazil uses GSM at 900 Mhz and at 1800 Mhz. If you intend to continue to use your Verizon service back in the US the prudent thing would be to buy a dual band 900/1800 phone such as is marketed in Europe and in Asia. If on the other hand you were to change to another provider such as cingular or T-Mobile a triband or quad band phone would be useful to you as it would be useable in both North American (USA/Canada and some South American countries) and in Europe and Asia as well. If you have no intention of changing US carriers a triband or quad band phone is really an unneeded expense and will be a a waste of your money.
A triband phone with 900/1800/1900 would likely work for you as well. A quad band phone is not necessary unless you are going to switch carriers in the US.
eBay or sometimes you can find them on craigslist. You can pay full retail from places such as expansys.com.
For information about prepaid in Brazil go to:
For Thailand: