No. Your Trip Leaders transport all luggage between hotels, where it’ll be waiting for you in your room (or in the hotel lobby, where staff will assist). Leaders will also gladly transport any new purchases you make along the way. You need only carry snacks, clothing and personal items for the day's activities.
On Biking trips, our bikes come with optional trunk bags for storing personal items (rain jacket, snacks, wallet, etc.). In our experience, wearing backpacks while riding isn’t very comfortable, so we limit our gear to what fits into the trunk bag. Should a day pack be best for you, our advice is to ensure it fits well and isn’t so big as to weigh you down over time.
For Walking & Hiking trips, a well-fitting day pack can be the difference between a good day on the trail and a great one. Seek a size large enough to carry layers plus snacks, water and small personal items, but not so big and heavy that it causes discomfort. Consider options for built-in compression straps, women-specific designs, and hydration compatible packs (where the use of a water bladder replaces the need to carry bottles).