I use the rawhide pieces(jaquima) because they are stronger and have their own lead-line(pisador) attatched. They are made with a standard rawhide bosal(nose piece) and barbada(curb piece).
You will find that there are a lot of single pieces available, the reason is that you will need different combinations of bosal/barbada, before getting your horse to reach the goal set. The jaquima will allow you to have one head set but to change the bosal or barbada without the need of another head set.
When teaching a horse commands such as stop, turn, flex, etc.; it is important that the horse is comfortable but does not overpower you. When you start asking of the ho rse through the riens, his first instinct is to pull or fight back. The following combos will hopefully allow you to understand better the pieces and their role in training.
The main idea is to have combinations with soft on top(bosal) and hard on the bottom(barbada) and vice versa. These combos will give the horse a sense that youare in control but at the same time they feel the reward throug the soft piece you may have on, regardless of which one it is.
Also it is good to have soft/soft and hard/hard combos available. When starting your horse, you should have a soft/soft combo. This is so that you find out the horse's sensitivity and their personality through the introduction of an unnatural change to their regular habitat.
The use of different headgear works in a cycle. Your goal is to start with a soft/soft and to eventually end with a bitted horse and a soft/soft head hear. The combos will be used at your own judgement.
The hard/hard combination is used for a very short time and only in extreme situations. If you are riding a horse no one else has worked with, the use of this combo may not be needed as often.