beat the crowd: Get something or do something you know many other
people are going to get or do but do it before them.
Example: if we go to the game early we can beat the crowd and get a
good seat.
dog one's steps: Something or someone which will not go away / leave you alone.
In the example you gave, ignorance and want are not things we wish to
have but we cannot gid rid of them.
a little death goes a long way: I don't know this exact saying but whenever we use the expression "a little . . . goes a long way, we mean we don't need to have much of something to satisfy us or make us happy.
