Below is an excerpt from "The Prairie Traveler" ©1859 regarding the types of arms one should bring on a trip across the plains and prairies. Along with some basic instruction of where to keep the weapons handy.
Every man who goes into the Indian country should be armed with a rifle and revolver, and he should never, either in camp or out of it, lose sight of them. When not on the march, they should be placed in such a position that they can be seized at an instant's warning; and when moving about outside the camp, the revolver should invariably be worn in the belt, as the person does not know at what moment they may have a use for it.
A great diversity of opinion obtains regarding the kind of rifle that is the most efficient and best adapted to Indian warfare, and the question is perhaps as yet from being settled to the satisfaction of all. A large majority of men prefer the breech-loading arm, but there are those who still adhere tenaciously to the old-fashioned muzzle-loading rifle as preferable to any of the modern inventions. Among these may be mentioned the border hunters and mountaineers, who can not be persuaded to use any other than the Hawkins rifle, for the reason that they know nothing about the merits of any others. My own experience has forced me to the conclusion that the breech-loading arm possesses great advantages over the muzzle-loading, for the reason that it can be charged and fired with much greater rapidity.
Colt's revolving pistol is very generally admitted, both in Europe and America, to be the most efficient arm of its kind known at the present day. As the same principles are involved in the fabrication of his breech-loading rifle as are found in the pistol, the conviction to me is irresistible, that, if one arm is worthy of consideration, the other is equally so. For my own part, I look upon Colt's new patent rifles as a most excellent arm for border services. It gives six shots in more rapid succession than any other rifle I know of, and these, if properly expended, are oftentimes sufficient to decide a contest; moreover, it is the most reliable and certain weapon to fire that I have ever used, and I can not resist the force of my conviction that, if I were alone upon the prairies, and expected an attack from a body of Indians, I am not acquainted with any arm I would as soon have in my hands as this.
The army and navy revolvers have both been used in our army, but the officers are not united in opinion in regard to their relative merits. I prefer the large army size, for reasons which will be given hereafter.
Below is a picture of an 1855 Colt Revolver the original picture comes from an antique arms dealers website. I'd also search for other Colt revolvers, it is more than likely that in 1859 the traveler would use a gun he or she purchased prior to the year they are traveling. Just my two cents.