Why did David choose to ingratiate himself into Caleb's family?

Because of his promise to Caleb and because he genuinely cared for the family.

I don't think David lied with all the talk about Caleb being his friend and he swearing to him to visit his family (he was on the photo afterall). Maybe he wanted to always stay for longer or maybe he really only wanted to stay for short. In fact the phone call he did might really have been the surgeon he wanted to visit right after checking by Caleb's family shortly, trying to start a new life just after that. But the family was more than happy to have him stay, having found somewhat of a replacement son in him.

And he wanted to genuinely help the Petersons, on the one hand because he felt responsible to take care of his late comrade's family, and on the other hand maybe because he seemed to grow more and more attached to them. But well, David being the quite deranged person he is, his means of helping the family were rather extreme, but they were always supposedly in their best interests, I think, from beating up Luke's bullies, getting Spencer's boss out of the way for Spencer's promotion and freeing Anna from her lazy-ass and unhealthy boyfriend (and he had to murder the gun sellers because they could implicate him easily, I guess). According to David (and he has no reason to lie to Mrs. Peterson right before killing her):

I wanted to help. I considered it my mission to assist you all while I was here. There were just too many complications.

He wasn't so paranoid about his identity until it started to crumble. Afterall, the Petersons didn't have much reason to blow his identity, for all they knew he was a former comrade of Caleb, and I guess that much was pretty true. It was only once he realized that his cover had been blown that he started to kill everyone, including the Petersons, since that was part of his mental programming, as Major Carver explains it:

David has neurological conditioning Miss Peterson, designed to protect both him and the experiment. If he feels like his identity may be compromised, he's programmed to clean up all loose ends. I doubt he could stop himself now even if he wanted to.

And even though he ultimately can't fight his own nature, we can see a bit of remorse in him when he apologizes to Laura and Spencer for killing them and when he tries to comfort Luke after he stabbed David, saying

You did the right thing, I don't blame you. Don't feel bad.

There are a couple of obvious signs that david is actually an android/robot of some sort:

1. He doesn't need much sleep.
2. Alcohol and drugs seem to have no effect on him.
3. He was able to consume that 'very spicy' drink at the bar scene without even flinching.
4. He got perfect aim! He needs only 1 or 2 shots to take out mercs in full body armor.
5. During the sex scene, the girl can't get him hard at first. Then he jumps on her and suddenly he's hard as if he just turned on 'pleasure bot mode'.
6. He does the 'terminator thumb up' when he supposedly dies at the end (perhaps a homage to T:2)
7. He survives severe injuries at the end.
8. His name is 'David'. (Used in a few other prominent AI movies.)

So maybe he's an android/robot version of one of Calebs friends (both experimented on) and his promise to david still lingers somewhere in his head between all the 'conditioning' done to his brain.

I believe it was because David actually was Caleb, his identity erased as part of the program and face reconstructed to look like a former squad mate. He felt the subconcious need to return home and help his family (who I'm sure he didn't conciously realize were his family) This makes the most sense to me, especially when he gives Luke a thumbs up in the final scene.

I don't see how the plot of the movie is so hard to understand. The Army guy explained to Anna in the car why David would have those special abilities. He clearly states that David was experimented on and they turned him into some sort of super soldier. After that David escaped but they assumed he was dead after finding the burned bodies and after that, the trail on him was cold until Anna called them.

I think that David was really Caleb's friend before he was experimented on and that he did promise to visit his family but he was chosen instead for the experiment.

David escaped to visit the family before having the plan to get out of town to meet the plastic surgeon. I feel like he also had a plan to help the family like he had promised and the things he did were just the ways he knew how to survive and protect. He beat up the bullies to protect the son, he framed Anna's bf after she told him, he killed the dad's rival so that he could get a promotion all to help the family.

I do think that by him being trained as a soldier when he was compromised he had no choice but to get rid of the people who put him in the compromising situation, as that's probably what he was programmed to do. I don't think he had any intentions of ever hurting the family until Anna started to snoop.

My theory on the whole David/Caleb thing is that he was actually Caleb but he had the plastic surgeon alter his face to look like a squad mate but whilst pretending to be David as from when Anna enquired to the Army, the profile picture of David was entirely different. This couldve been a double red herring on his part; fake his own death but act under his squadmates name as to lead them in a different direction. If they knew he (Caleb) survived the most probable place he'd go first would be his hometown to his family.

Psychologically that is sound, they conditioned them to cover their identities, whenever Carver confronted David he probably reasoned that he could've altered his appearance and therefore was not surprised when he looked different but never suspected he could have been Caleb which is why he said anything to Anna. Also, need to know basis.