One big distinction is active vs passive noise cancelling (passive can also be called noise isolating). Active involves a microphone taking in outside noise and actively feeding cancelling sounds into whatever you're listening to. The things to consider here are a) requires a power source like batteries and b) works best when the outside noise is consistent, like riding on an airplane, as opposed to inconsistent noise like attending a baseball game.

Passive uses only its closed back ear cups and sealing ear pads to passively keep out outside noise. Nothing fancy, just a physical barrier, no power required.

A good, cheap option for passive is the Sennheiser HD 202. And the sound quality and comfort will go up with Sennheiser model number (and price). The 202 (which I have and use) is fairly comfortable and gives good sound quality for the money (about $22, or less when on sale). If I was buying a pair right now, I'd probably go for the HD 429 which is $38 on Amazon. I haven't used them, but they have bigger pads and go over the ear more, and are supposed to have better sound quality. That would be worth the extra $16 to me.

I'll have to leave it to someone else to recommend an active noise cancelling set...I don't know.
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http://i.imgur.com/81XSukd.jpg <-- Happy trails