How does this look so far, along the right lines?
Yes. You should have two booleans, though, started (in place of storeString) and ended, set to true when the end of packet marker arrives. Leave started set to true when the end of packet marker arrives.
Then,
} // end of serial data collection
if(started && ended)
{
// A complete packet has arrived
I have done some reading around but cannot suss out what the next stage is.
strtok() and atoi().