As adidaskid808 mentioned, you have the option to purchase a microSIM adapter online, which allows the SIM to be used in the larger SIM slot of the "cheap" phone. Sometimes the adapters themselves can be of cheap quality (and price), so I would only recommend using them for a short period of time, especially if you plan on switching your SIM back and forth.
Your other option is to pay a visit to an AT&T corporate store and ask if the employee(s) there can transfer your account information over from your current SIM to a standard sized SIM that would fit the larger slot of the new phone. Ideally, everything should go smoothly during this process.
Your other option is to pay a visit to an AT&T corporate store and ask if the employee(s) there can transfer your account information over from your current SIM to a standard sized SIM that would fit the larger slot of the new phone. Ideally, everything should go smoothly during this process.