Why did Hank Pym choose Scott Lang?

Hank Pym had a job that required a very specific set of skills that aren't very common.

• He needed someone skilled at breaking in to things. Someone who knew how to get around without being noticed. Someone who could plan ahead, but improvise when things went south. Perhaps someone who could hold their own in a fight. In other words, he needed a thief.
• He needed someone technical. The Ant Man suit is a highly advanced piece of machinery. He needed someone who could at least basically understand the technology behind the Ant Man suit. On top of that, the security systems at Pym Technologies is highly advanced, so he would need someone with a lot of technical ability to get through it.
• He needed someone willing to help. This job was dangerous and, to put it lightly, unconventional. Not many people would be willing to take on the task.
• Expendable. Hope could have easily have done this, but after losing his wife, Hank was not about to send her on a dangerous mission.
• Honest. He had to be sure that whoever he was giving this tech to was not going to turn it around and use it for nefarious reasons. After all, the whole point of the mission was for his tech to not fall in the wrong hands.

Meet Scott Lang:

• He was an experienced thief: Check
• He has a masters in Electrical Engineering (at Stanford?): Check
• He was working at Baskin Robins and desperate to get his good name back so he could see his daughter: Check
• Hank doesn't really care about Scott: Check
• Generally a good guy. He was a sort of Robin Hood who burgled for good. He also took great care to make sure he did not hurt anybody during his burglaries. Check.

While it's not shown in the movie, it's not a hard stretch to assume that Hank had a few candidates in mind. He was probably observing all of them over time. We do know that Hank was watching Scott already based off this quote (found by Johnny Bones in the comments):

Scott, I've been watching you for a while. Ever since you robbed Vistacorp. Oh, excuse me, burgled Vistacorp. Vista's security system is one of the most advanced in the business, it's supposed to be unbeatable but you beat it.

Vistacorp most likely has very similar security measures as Pym Technologies. From that, it's safe to assume that Scott has gotten further than anyone before.

Hank set up the break in on his house as a sort of final job interview to see if Scott could pull it off. It was also a convenient excuse to get Scott to him so they could meet.

Scott is not a crook, he is a vigilante. This is important, because despite being expendable he needed to be trustworthy. Hank Pym is giving him access to some of the most valuable technology on the planet, not excluding alien or wakanda tech. If he turns around and kills Hank and Hope in order to get exclusive access, then that’s not a good thing.

He needs to not only be willing to attempt the mission, he needs to believe in it and be willing to commit to it.