Let's start with you second question, because I think that's easier to answer:
Here are the plausible defenses against Run and Gun: 3-2, Man-to-Man, 1-3-1.
They are all used in different situations.
If your man-to-man defense already HAS good enough perimeter defense and your opponent has a decent inside game and rebounding, you'll want to go man-to-man.
If your opponent's offense is really bad inside but has great outside shooting, while your defense isn't that great ouside, you'll want to do a 3-2 zone. It'll give you a good boost to perimeter defense while your inside defense and rebounding take a slight decrease.
1-3-1 is an extreme case of 3-2. you'll get a great boost to perimeter defense but your inside defense and rebounding is mostly left up to your center, so either get a great center or make sure your opponent doesn't have a good inside game.
Now, to your first question: obviously you want to concentrate on your outside: Run and Gun and Motion concentrate on jumpshots, while Run and Gun takes a lot more 3 point attempts and is a faster pace. I don't know anything about how princeton works, so I can't say anything about that...
If they're outside defense with 2-3 zone is going to be horrible compared to your outside shooting, then use motion because of its slower pace. The slower pace means that you'll always be taking quality shots and while you might not score as many points, your opponent won't have the ball as much since you're not taking quick shots and you'll make the most out of every posession.
If their outside defense is going to be comparable to your outside game, go with run and gun. Since it's quicker paced, you won't have the problem of your players holding the ball for too long and taking a bad attempt as the shot-clock winds down.