Very few are completely noise-cancelling. The best will always leave something, although often distanced and muted enough not to be a bother. At the very worst, I have been known to use both earplugs and headphones at the same time and even then some stuff got through.
In terms of headphones. If you don't need audio, look perhaps for those used by gun enthusiasts. But, if you are looking for ANC and audio, I'm afraid, in this case the more you spend, is definitely the better. Sony and Boche definitely lead the pack with their highest priced models. Although, seeing as there is little difference between the absolute latest and the previous model, you can save on getting the previous one, without making a massive difference in the ANC.