I do not have any experience with gsm modem in communication with microcontroller, but I am almost certain you need connect RX and TX pins directly to sim300.
If you see pins configuration of used microcontroller - ATmega8, you will see there are separate pins for RX and TX function. If you read datasheet for this microcontroler (link is in the name of microcontroller in this sentence), you will see next text:
For TX function The USART Transmitter is enabled by setting the Transmit Enable (TXEN) bit in the UCSRB Register. When the Transmitter is enabled, the normal port operation of the TxD pin is overridden by the USART and given the function as the Transmitter’s serial output. For RX function The USART Receiver is enabled by writing the Receive Enable (RXEN) bit in the UCSRB Register to one. When the Receiver is enabled, the normal pin operation of the RxD pin is overridden by the USART and given the function as the Receiver’s serial input.