Simple. Since you already mentioned using a Basic Stamp for the trigger, why not use it for other stuff too? Get a phone that, when connected to a serial cable, acts like a Hayes compatible modem (they exist). Have the serial cable connected to the Basic stamp which is also monitoring another serial line that goes to the GPS. You can call it to trigger it, then it'll call the computer you specify and start uploading coordinates.
If the phone supports GPRS (not related to GPS, it's a network protocol) you might be able to command it via serial to upload the data to a server on the internet.
The basic stamp can be your computer that takes the GPS data and does whatever you want with it. Hell, you could even have it so when you call the phone, the stamp outputs DTMF tones of your current coordinates through the soldered mic input on the cell phone. All you need to do is use a DTMF decoder (you can get/build a handheld one easy) to convert it into digits. That way, you just call the phone from your cell phone, get a read out of the coordinates, then repeat as needed (if it's moving) without needing to go home again.