It was obvious what King and others were marching for back then: equality and justice for black people, and for improvements to their lives. In the 60s, Black people were still basically the next level up from slaves - absolutely shameful.
Correct. The civil rights march was to draw attention and increase support for the civil rights act.
Unfortunately, many people's view of history will probably now be based on the portrayal of LBJ in the movie "Selma" where his role was mischaracterized for racial effect (it doesn't fit todays narrative). The reality was different, the march was an essential tactic to bring about change, not just a march for the sake of it (and the people marching were putting things on the line, not just having a nice day out):
The makers of the new movie “Selma” apparently just couldn’t resist taking dramatic, trumped-up license with a true story that didn’t need any embellishment to work as a big-screen historical drama. As a result, the film falsely portrays President Lyndon B. Johnson as being at odds with Martin Luther King Jr. and even using the FBI to discredit him, as only reluctantly behind the Voting Rights Act of 1965 and as opposed to the Selma march itself.
In fact, Selma was LBJ’s idea, he considered the Voting Rights Act his greatest legislative achievement, he viewed King as an essential partner in getting it enacted — and he didn’t use the FBI to disparage him.
On Jan. 15, 1965, LBJ talked to King by telephone about his intention to send a voting rights act to Congress: “There is not going to be anything as effective, though, Doctor, as all [blacks] voting.”
Johnson then articulated a strategy for drawing attention to the injustice of using literacy tests and other barriers to stop black Southerners from voting. “We take the position,” he said, “that every person born in this country, when he reaches a certain age, that he have a right to vote . . . whether it’s a Negro, whether it’s a Mexican, or who it is. . . . I think you can contribute a great deal by getting your leaders and you, yourself, taking very simple examples of discrimination; where a [black] man’s got . . . to quote the first 10 Amendments, . . . and some people don’t have to do that, but when a Negro comes in he’s got to do it, and if we can, just repeat and repeat and repeat.
“And if you can find the worst condition that you run into in Alabama, Mississippi or Louisiana or South Carolina . . . and if you just take that one illustration and get it on radio, get it on television, get it in the pulpits, get it in the meetings, get it everyplace you can. Pretty soon the fellow that didn’t do anything but drive a tractor will say, ‘Well, that’s not right, that’s not fair,’ and then that will help us on what we’re going to shove through [Congress] in the end.”
King agreed, and LBJ added, sealing the deal, “And if we do that we will break through. It will be the greatest breakthrough of anything, not even excepting this ’64 [Civil Rights] Act, I think the greatest achievement of my administration.”
Their march was to demonstrate the problem that the legislation being put forward was going to change, to shift public opinion. It had a clear goal and achieved it.