GSM modules or WiFi?
If your final product is designed to be worn outside you have to go down the GSM path as it work in a wider range. If it is indoors only Wi-Fi is more appropriate.

The reason is cost. GSM covers a wider range, but it requires a more expensive module, and you also have recurring costs from the cellular carrier and running a publicly accessible server (since you need at least either a static IP address or a domain name, and either of them cost money.) Wi-Fi, however, covers only inside and immediate around the building the access point is set up, but requires only a cheaper module, and since it is, after all, LAN, so there is no recurring cost other than electricity bill (which you also have to pay if you go down the GSM path anyway)