I thought this already had been answered, but here it is again:
The Caye Caulker Water Taxi boats at the Marine Terminal are open boats, but your luggage may get put up in the bow and protected from the weather, or it may be placed in the middle of the open boat. A couple of the other ferries do have some cover, but if it's rainy and stormy you're likely to get wet anyway and maybe seasick. If the weather's bad you may want to fly. If the weather's sunny and calm it's a nice little ride. You'll get to see Caye Chapel and Caye Caulker as you pass by on the way to San Pedro, and you'll probably make a brief stop at Caulker.
These are working water taxis, used as much by locals as by tourists, not party boats, so there is no rum punch.
The trip takes an hour and a quarter. The Caye Caulker Water Taxi boats leave from the Marine Terminal near the Swing Bridge (you can walk from the Radisson but with luggage it would be better to take a taxi), and most of the other boats also leave from near the Swing Bridge.
Cost is US$12.50 per person one-way, kids half-price.
In theory you can call and make reservations, but in practice it's often first-come, first-served.