Watching Aliens won't help you understand Prometheus, since it doesn't have anything to do with those movies, per se.
The biggest misconception about the movie is that it takes place on the planet from Alien and that the creature at the end is one of the creatures from Alien, called xenomorphs. Neither of these is true, which explains why people are confused about how they connect to Alien. The planet in Prometheus is LV. 223, the planet in Aliens is called Acheron/ LV.246.
I assume that you understand all the stuff with the scientists, since it is pretty straight forward. In addition to Weyland wanting immortality, he also wanted alien teraforming technology, which was part of why he kept the mission a secret.
The reason David betrayed the crew is because he hated his own creator because he could not be human. That's the central theme of the movie, the basic biblical concept of man's Fall from Grace.
The basic story is that the alien Engineers have this stuff, the Black ooze, that rapidly accelerates mutation/ evolution. They went around and used it to seed life on barren planets throughout the galaxy, including Earth.
The movie doesn't infer why, but somehow they gained the ability of the Black Ooze to be used as a weapon. I believe that it was because the ooze reflects the spiritual state of it's user, and so if it is used by the corrupt it will create monsters, as seen in the movie.
The Black Ooze is what created the Xenomorphs from the Alien movies, but it is not known whether they were created by the Engineers or came about independently of them.
The Engineers saw that humans had become corrupt and so they wanted to unleash the Black Ooze all over the earth to destroy them. I don't remember exactly why, but for some reason they failed to do this. Maybe it was because they became contaminated by the ooze and set the whole operation into stasis where it was abandoned for thousands of years and that's where the scientists found it.
It's not alluded to in the movie, but the theory is that contact with the xenomorphs destroyed the Engineers homeworld, which was why they abandoned the installation/project on LV. 223. One of the Engineers infected with a xenomorph parasite crash landed on the planet Archeron/ LV 246, where it was found by the crew in the first Alien movie.
Prometheus takes place 28 years before Alien, but the implication is that the ship on LV246 has been there for thousands of years. In other words the "alien" and ship at the end are not the "alien" and ship from Alien.
There is no art in me. There is no kindness. For art is humane. And I am inhuman.
This weapon will replace my tongue. I will learn to speak through it. And my poetry will now be written with blood.