Your watch will only work via your iPhone (tethered) then your iPhone’s network connection is either via WiFi or cellular that’s if you have a phone carrier plan.
Are you able to manage your watch from your iPhone using the Watch app? If you can’t then you won’t be able to leverage any app that needs a internet connection like the stock market feed. Beyond that you don’t have a full web browser so many web sites won’t work on your watch if you launch a URL link.