At some units you could be out on detail almost everyday, other units only a couple of times a week. The details could range from 8 hour drives with a 45 minute break or just half hour jollies, in vehicles from civvy hire cars to 15 Tonne DROPS with a trailer. On Exercise or Operations (such as TELIC) you could be driving up to 20 odd hours a day.
As for the stores side of things you could end up running or working in a store but that is very unlikely to happen for a few years. As a new driver you would mostly to doing driving or the day to day servicing of vehicles.