I'd like to find the name of the tool that I would need to measure the inside of all of my barrels, so i can buy the best bullets to reload for each gun.

what is this measuring device called?

Best way I know is to "slug" the barrel. Get a soft lead bullet for lack of a better word and use a wooden dowl to basically pound the lead slug thru the barrel then measure it with a micrometer. Others may know of better ways. Brownells and others have slugging leads/bullets.

The slug method is indeed the way to go.
But then, what do you do with it? Usually such measurements are only taken, when there is a gun of an unknown caliber.
I would assume that you know for which cartridges your guns are chambered. The knowledge of slight manufacturing variances regarding the inner diameter of your barrels will not really make you any wiser when it comes to reloading.

It is usually only done to older black powder type rifles and or old military rifles when one wants to cast bullets of a specific diameter. If it is for a modern rifle, other than cast lead bullets it is of little use. At higher velocitys a soft lead bullet will really foul the barrel quickly. Usually 2000fps or so.

HTH

Ron