Most people are not aware what bit is suitable for their horse.
What discipline do you ride your horse in? - Dressage (flexion), Cross country (strength), Showjumping (control) etc.
What your experience/skill in riding is. - You don't want to ride in a Weymouth if you have no experience in double bridles as this can be very detrimental to your horse.
The capability of your horse. - If your horse has only ever been lightly back and you put him in a gag this may be to severe for him.
The shape of your horse's mouth. - Always make sure your bit fits perfectly.
Most horses should be able to ride in a snaffle as it's the mildest form of bit that allows clear communication, but if your horse requires a more severe bit you need to take a lot into account. Finding the perfect bit for your horse requires trial and error. Is the bit definitely the reason for your horse's misbehaviour? What is the reason for changing your bit? (strength, flexion, rearing etc.)
First of all what size and shape do you need?
Horse's mouths are all shaped differently so what may be comfortable for you friends horse may not suit yours. You have measured your horse's mouth at 4”. So you just need a 4” bit right? Wrong. You also need to consider the shape and strength of your horse's mouth. Does he have a low palate or narrow gap between both teeth? Has he got a hard of soft mouth?
Traditionally, people use the 'one wrinkle' rule to determine whether the bit is the right size. In most cases this is correct, however there is more to just 'one wrinkle'. The bit should sit comfortably across the bars of the horses jaw (The part of the mouth with no teeth) and it should be even and balanced on both sides. A horses behaviour could usually tell you whether the bit fit's correctly or not; Mouthing the bit or carrying their head to one side are common signs.
For Example: I have a Welsh sports horse which I compete in 3 days events and I want to find the perfect bit for each discipline. I have my riding boots, show jacket, shirt, stock and Riding hat that all fit perfectly. I need my horse's tack to fit perfectly too in order for him to perform at his best and a correct bit is essential. In dressage he has trouble flexing so after trying different bits I found a jointed Pelham worked great. In cross country he can be very strong, so I use a Cambridge Kimblewick, In showjumping I use a twisted eggbutt for good communication and control.
By using a different bit for each discipline he remains comfortable whatever we are doing.
What types of bits are there? Snaffle - Pelham - Weymouth - Kimblewick - Curb - Hackamore
Of course you can always use a bitless bridle if your horse doesn't like using a bit!
You should always get an equine dentist to examine your horse's teeth and get a recommendation on what shape/size bit is suitable for your horse. A horse misbehaving is not always down to your bit, weigh up all possibilities. It could even be that your bit is too strong and causing pain.
I had a friend who bought a horse that was being ridden in standing martingale, dutch gag and flash because 'it was to strong and continually throwing his head up' after removing all of this unnecessary tack and putting him in a french link snaffle he has been perfect.