https://en.wikipedia.org/wiki/History_of_New_Mexico

This is the story of a young man (age 21) who travels back in time from the early 21st century to 1881 to the Territory of New Mexico.  More specifically, he travels to Albuquerque for this is where he was from in the 21st century.  New Mexico won’t be a state until 1912.

Homesteaders began moving into the area in the late 1870’s as the trains finally begin to reach the region.  The train reached Santa Fe in 1880, later Albuquerque, and Deming in 1881.  The New Mexico Education Association is formed in 1886.  The first colleges open in 1889.

Note:  The Homestead Act was in 1862.

You are a young woman (18-23) that has either grown up in the region or moved here during this turbulent era.  You can live on a ranch or in town.  But I am using Albuquerque as the focal point.  (It starts its boom in 1880-81.  Crime sky rockets in downtown until they finally get a Marshall.)  You can even be foreign and have immigrated with hopes of living the American dream.  I enjoy characters that represent a little imagination and creativity, so I don’t want to tell you what to be.  Big ranch owner’s daughter?  School teacher?  (Civil War anything doesn’t fit because of time.  You would have been a child.)

History Brief
(Billy the Kid’s big period was 1878-1880.)  I would avoid being Hispanic (neuvomexicanos) as they were second class citizens.  Native Americans had it worse.  Slavery and even indentured servitude was outlawed in New Mexico in 1862, but blacks are less than second class citizens in this time.  Same is true is just about anyone not White really.  And women won’t get to vote until 1920 in New Mexico.

Our young man is age 21, unfamiliar with colloquial mannerisms, speech, clothing, costs, culture.  But he has studied the history of the period rather heavily and recently.  He stands out in a crowd without trying.  He is 6’7” built like a football quarterback, short black hair, sharp blue eyes.  He walks with a limp (left side) and wears a fingerless deerskin leather glove on his left hand.  

He is well armed with both rifle and pistol - a Peacemaker.  He has already bought - at far too high a price - a neighboring homestead.  It is far from the best land in the region.  Most ranchers would say he was taken.  Most will expect his ranch to utterly fail.