I wouldn’t especially recommend noise-cancelling phones. They are generally not as good as regular headphones at the same price point. And really good closed-back headphones can give you a good sound isolation.
If you’re in an office or other shared setting, closed-back headphones are the best way to go. Not only do they keep noise out, they don’t broadcast to your neighbors what you’re listening to.
Open back headphones usually have the best sound quality but they’re best suited for listening in quiet, private environment (e.g., a home office).
If you’re listening with your iPhone or computer, you’ll want headphones that have 1/8″ (3.5 mm) jack.