I'm just going to pipe in here about the contact issues because there is a bunch of misinformation being strewn about on this thread.
First of all, lunging in side reins is going to be beneficial to getting the horse to accept the bit. And not floppy side reins, they need to have a nice contact to them, and be adjusted such that the horse will always be looking to the inside, regardless of anything.
Once you are in the saddle, your hands are actually too busy. They need to be either rooted onto the neck, holding onto the saddle pad or resting onto the saddle. Your reins need to be short enough that you have a good contact (a few lbs) and can steer and adjust without moving your hands. I know there are people who disagree with me about this - but our goal is to have the head and neck still in relation to the withers in all gaits. The only way to develop this is with a hand that does not follow the head or neck - but follows the withers. The big pumping motion you see by lots of riders trying to "follow the mouth" and "be soft" is actually more disruptive and incorrect than a hand which is too stiff. On the contrary, the way you are using your hand to pull down and be moving in that direction is putting too much pressure on the bars, and causing the gaping. However, if the horse raises the head, your hands must stay rooted to the neck/saddle pad/saddle and not move.
Once you can keep your hands still and in one place, then and only then can you take them other places. And that is also only once the horse is consistent in a contact.
If you keep moving your hands (yes, even under the guise of following the horse's mouth) you will create a hard mouthed horse who is ridden front to back. Every movement you make with your arm is an aid, and it rides the horse from front to back and desensitizes his mouth. Your arm does not move, your upper arm is a part of your upper body and your elbow should always be in contact with your sides, and as an extension your hands should be quietly following the wither, which is by all accounts relatively still as well.
PS it is also very hard to develop a contact in the walk. The horse has an easier time coming into a contact in the trot and canter, and also play with transitions!!
Remember the hands do nothing unless you need an aid, just like the legs and the seat. Only ask for what you want if you mean it and otherwise be still :)
They say money doesn't buy happiness -- well happiness doesn't buy horses!