For the most part, the command set for GSM DCEs is standards based, so you will find useful libraries and examples of code that you can adapt or even just use as-is to talk to your modem. One library is here:
http://labs.arduino.cc/GPRS/Index
Except for the MEGA type, Arduinos have only one hardware serial line. So if you have to talk to the PC on one and the modem on another, you will have to either use software bit-banging serial on one side or the other, or move to a MEGA.
Arduinos have very little RAM, so using one for something that requires queuing of data is maybe not a good fit. Just 10 SMS messages could use most of the memory on an UNO. Again, a MEGA type would be a better fit.