G'day, and welcome to the forums mate 
For your particular question, it works the first way you describe - a person with an assault 3 weapon can fire three times, and then assault. Remember that you can only charge the unit you shot at, so you can't shoot one unit and different one.
As for the restrictions on changing weapons, there aren't any. You can only fire one of your shooting weapons in the shooting phase, and you can only use two close combat weapons (or one two handed weapon) in the assault phase, but you can shoot with one weapon, charge with the other. So your Nob can fire his shoota, then charge in and use his Power Klaw, without worries.
At any rate, future questions should be put up in the "40k rules Questions" section of the site, but since you're here, why don't you introduce your self a little? What Orks have you got, what are your friends playing, how long have you been playing, and so on?
Anyway, welcome again, and I hope I helped a little!
For your particular question, it works the first way you describe - a person with an assault 3 weapon can fire three times, and then assault. Remember that you can only charge the unit you shot at, so you can't shoot one unit and different one.
As for the restrictions on changing weapons, there aren't any. You can only fire one of your shooting weapons in the shooting phase, and you can only use two close combat weapons (or one two handed weapon) in the assault phase, but you can shoot with one weapon, charge with the other. So your Nob can fire his shoota, then charge in and use his Power Klaw, without worries.
At any rate, future questions should be put up in the "40k rules Questions" section of the site, but since you're here, why don't you introduce your self a little? What Orks have you got, what are your friends playing, how long have you been playing, and so on?
Anyway, welcome again, and I hope I helped a little!