in general, backend life becomes way, way easier if you just store everything in zulu time, transmit in zulu, and localize it on the frontend (which is what javascript does by default anyhow, iirc).
maybe there are some cases where you want to store the timezone (e.g. you've displayed a datepicker and the user has expressly entered a timezone)--but normally you'll save headache by storing everything in zulu time.
if storing the timezone is important for those transactions, then I could potentially see that as warranting storage with a timezone as well.
basically, ask 'if the timezone matters' with respect to the information being encoded. if it's just for display purposes and can be ignored, then KISS.