BrownBear: np!
Aaaaand here, HeroicPenguin is likely referring to the HD
25-1, as opposed to the cheaper (and nearly universally considered inferior) Sennheiser HD 25
-SP.
OP, here's the skinny based on your requirements:
- "Noise cancelling"--forget cancelling. This means stuff like Bose, which uses additional batteries (in the headphone or in some in-line volume control) to process external noise and cancel. You pay extra for that, and it tends to result in lower sound quality. Instead, look for noise isolating headphones. These just naturally block noise out; kind of like closing a door blocks out some noise from the hallway. With a good enough block (or "seal") and music playing, you'll barely hear anything.
- Closed back--some headphones have vents or grilles on the earcups. You don't want that. You want earcups made of solid material, opaque and no holes all the way through, to help with noise isolation.
- Headphones to sleep in--could be a bad idea, man. What happens when you turn on your side in bed? Some people have reported that they sleep with earphones on, but headphones?
- Amplification--I know you didn't ask anything about this, but just trust me: sooner or later someone is going to say you some headphones need an "amp". The simplest, most time-and-money efficient you can do right now is to remove all those options. These sound like your first major headphones, so keep it simple...there definitely are headphones that do what you need without having an amp. Go unamped; if you want to dabble with amps, do it later.
tl;dr version:Search for "closed unamped bass" on the forums, you should find enough results there.