Nearly every climb uses a simple combination of gloves. I generally carry a liner glove, a fleece glove and a waterproof warm glove on every trip. However, I do supplement this combo with other things in special circumstances. On training trips -- those where you practicing self-arrest and crevasse rescue -- sometimes I'll bring an extra pair of fleece gloves because things get so wet. On expeditions, I carry thick mittens in addition to the basic combination. And when I think that an alpine rock climb will be cold enough that I need to wear gloves, I will often bring a pair of tough leather gloves.
As for leather gloves, any tough pair of gloves will fit the bill. I use a large pair of belay gloves. They are big enough that I can still fit my liner underneath.