Wordpress-like Subscription
I would consider this carefully from a subscriber's perspective. i.e. If I received an email every time something was published, I may consider unsubscribing very quickly.
An alternative which I've found works very well is to send email updates on a regular basis - that way your subscribers have an expectation of the frequency.
We've used Campaign Monitor to automatically pull content from a RSS template and then send an email newsletter as well. You also have the flexibility to curate the entries as you see fit.
Have a look at this page/video: https://www.campaignmonitor.com/blog/new-features/2012/03/one-click-content/

Ability to sign up per channel via email (a form per channel)

You can create separate (subscriber) lists within Campaign Monitor, for each Channel/Section

Confirm email address (double opt-in)
No (site) registration necessary
Ability to unsubscribe

These are all possible.

Auto send email notification when new entry is posted

Automation is also possible.
Hopefully that makes sense - let us know your thoughts?