As far as the AT commands are concerned, you should get the following...
Text mode and sending ok:
PDU mode and sending ok:
where "mr" is the message reference value.
Just that should give you some sense of whether or not the SMS got there.
Or you could *also* use settings to request a status report, and then if the message reaches its recipient, you should get a status report, referring to the message with the "mr" value you got when you first sent it.