The movies do show Darth Vader wanted power, and that he was power hungry even as Anakin. Anakin's quest for power is multi-faceted, and doesn't just hang on his lust to rule the galaxy. Anakin searches for personal power, so that he can satisfy is own greedy ambitions and feelings. His lust for rule comes later, only after everything that he wanted personal power for has been taken from him.
In Attack of the Clones, in Padme's apartment Anakin starts off complimenting Obi Wan as a mentor, saying he is as powerful as Mace, and as wise as Yoda. However, Anakin quickly turns those compliments around onto himself when he says that in many ways he (Anakin) has passed Obi Wan. He then goes onto complain that he is ready for the trials, and it's Obi Wan holding him back. Wanting to take the trials is a quest for more power. While it is a natural quest within the Jedi Order to want to take the trials, you can see from the entire conversation that Anakin's quest for the trials is driven by his arrogance because he feels he has already obtained a certain amount of power, and Obi Wan is an obstacle to more power.
Staying with AOTC, in the picnic scene we see a political side of Anakin and where he stands as far as political rule. Granted these ideas are planted by Palpatine, Anakin still agrees with them. Anakin says that someone wise should be able to sit down and make politicians do what is best for the galaxy. As I said this is obviously Palpatine's teachings, and Anakin tells Padme that it shouldn't be him that is the one tells people what to do, however, as we get into later movies we see that this line of thinking changes. The picnic scene is important because it's a hint of Anakin's thought process of those who are in power and what they should do to maintain order with their power.
In the garage scene in AOTC, Anakin is upset because he feels he could have saved his Mother, which is an understandable emotion, especially for one that has these superhuman powers. However, Anakin doesn't stop there, he goes onto to say that one day he will be the most powerful Jedi ever, and he will be able to stop people from dying. This is a pretty ambitious statement to make, and again points to Anakin's lust for power to satisfy his own greedy emotions. Once again Anakin makes Obi Wan the obstacle to power, rather than Anakin realizing there is a natural and normal progression.
At Shmi's funeral Anakin proclaims that he wasn't strong enough to save his mother, and makes a promise he won't fail again. Once again, a mindset that he will find a way to become powerful enough to stop people from dying...
So then we get into ROTS. A big part of the plot centers around Anakin trying to figure out how to obtain a power to save Padme. While it is only natural to not want the ones we love to die, we as humans are forced to accept death. However, Anakin feels that he should be powerful enough to not have to accept Death. So he lusts after that power. As Yoda warns him, those feelings are the shadow of greed because eventually the emotion becomes inward in that you want save people to stop yourself from feeling pain, as opposed to trying to save people for the purpose of saving people. Anakin, tells Yoda he won't let the premonitions he has come true.
In the scene where Anakin is late to the report on the outer rim sieges, Obi Wan tells Anakin that the Senate is expected to grant more powers to Palpatine. Anakin thinks this is a good thing, he fails to see that power to only one man is a bad thing. While at this point it isn't a personal quest for Anakin to obtain that power, it does setup later scenes in this movie and another as to how Anakin feels about power once he does want the power to rule.
Then there is the opera scene where Palpatine plants the seeds in Anakins head that there is a path to a power that Anakin searches for. Which then is played on again in the Chancellors office when Palpatine reveals to Anakin that he is the Sith Lord and that he knows the power to save his wife. This lust for power, a power that has been placed at Anakin's finger tips (or so he thought), is what eventually leads to Anakins fateful decision. It's Anakin lust for greater power to do things that no other Jedi can do, is what, in part leads him to the Dark Side. Anakin does unspeakable things to obtain the power he lusts after. In fact earlier in the movie, in Padme's apartment, Anakin reveals to PAdme he isn't the Jedi he should be because he wants more, and he knows he shouldn't.
However, his lust for power doesn't stop with his turn to the Dark Side. In fact it grows...
On Mustafar, after Anakin has cemented his turn to the Dark Side, we have Anakins temptation of Padme. Anakin brags that he is becoming more powerful than any Jedi, and that he is doing it for Padme, which is a lie. We now see that Anakin lusts after a greater power that isn't just about saving Padme, he now wants to rule the galaxy with Padme at his side. He tempts Padme with the power to make things just the way they wanted because he can kill Palpatine and take over. We finally see something that was buried deep down within Anakin , that only came out once in while (Attack of the Clones Picnic Scene). That being that Anakin thinks the right way is his way only, and that he is the only person that can make things right, in his own vision. This is the lust for power to rule the galaxy, which is the way of the Sith. Don't forget what Anakin says to Obi Wan right before they duel... "I have brought peace, freedom, justice, and security, to my new Empire"
Then we get to Empire Strikes Back with the temptation of Luke. Once again, Anakin (Vader) shows us that after all these years he still lusts after ruling the galaxy and shaping it into what he wants it to be, which is a lust for power:
" Luke, you do not yet realize your importance. You've only begun to
discover your power! Join me, and I will complete your training! With
our combined strength, we can end this destructive conflict, and bring
order to the galaxy."
" Join me, and together, we can rule the galaxy as father and son!"
So we see that after all these years, Anakin still wants to overthrow the Emperor and rule the galaxy, however, it is because of the injuries he suffers on Mustafar that he hasn't reached the level of power he once thought he could. Thus why he needs Luke. He doesn't see Luke as a son (at least not at this point), so much as he sees him as a tool to his own quest to obtain more power. Again, everything I would imagine a Sith is...