Belay devices are amongst the most important pieces of climbing equipment and also one of the first things new climbers tend to buy, so it pays to take some time and make the right choice. Standard two-hole devices like the Petzl Reverso 3 and Black Diamond ATC allow you to belay and abseil off single and double ropes. They're light and versatile, and equally good for sports or trad climbing, or even ice. Every climber should have one.
Petzl America Pro Traxion P51A
Figure 8 descenders are more for rappelling than belaying but if you're making a long descent on a hot day the extra metal on a fig 8 will disperse heat better than a smaller ATC-style belay device. They do have a tendency to twist ropes though. For big walling and rescue applications it might not be just about getting your body safety up to the top of a route. You might need to haul heavy gear (or a heavy person) behind you. Sometimes you might also want to ascend a single rope rather than a rock face, and for this we recommend Petzl Ascenders. A pair of left and right Ascensions will make the job just about as efficient as it can be. Pulleys can also be really useful when hauling, and again, Petzl make what are probably the best on the market today.