You see things like Jesse James who was heavily influenced by the events of the war or the fact that the railroad became a vital point to the Unions success during the war and it's boom in later years.
How did it affect people going west or the general politics of the era?
You're gonna have a hard time getting any kind of a comprehensive answer to this question, as it's just too broad of a topic. It would be like asking, "what kind of an impact did World War II have on America in the second half of the 20th century?" The question itself is so open-ended and complex that you could run in any number of directions trying to answer it.
For example, one could write at great length at how the role of women changed in American culture, specifically west of the Mississippi River, following the Civil War. One could go on for ages talking about the evolution of racial opinions and ideals out "West" following the Civil War, and how ideas of "whiteness" came into focus in a sort of mass hegemony that eventually eliminated notions of "German," "Dutch," or "Italian" in favor of just "white." How do you define "West," too? Is it by time period as well as region, and if so, what region and what time period?
I don't mean to discourage discussion, but it might help to focus your question into something that's a bit more digestible. You mention how the war affected people going west, and "the general politics of the era." What politics are you referring to? State or federal, and in relation to what?