Which key to bind to avoid conflict with native browser shortcuts?

For a pragmatic solution, copy Google. They have keyboard shortcuts in Gmail (and probably other products) that do a pretty good job of avoiding browser shortcuts.

If you only need keyboard shortcuts outside of form elements having focus, I would use plain letters (no Ctrl / Alt / Shift / etc.). Regular characters are only important to the browser if a form element has focus. Otherwise they're ignored.

For example, if you have paginated content, P could be previous and N could be next.

(Not sure if this would completely solve your problem because this won't work when a form element has focus.)

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Based on your comment (the focus will be inside a textarea), I would suggest a single letter chosen for each action with a different Ctrl / Alt / Shift combination per browser. Most people only use one browser, so for each user to learn just their own combination isn't a big deal.

So, for example, Ctrl + Alt + N in one browser might be the same as Alt + N in another.

The first thing I would test, though, is Shift, because most built-in combinations don't use one, but I don't know if the combos are always case-insensitive. Also watch out for OS-specific combos.

Here's what I've found mostly available so far:

OS X    - FF/Safari/Chrome - ctrl-[key]
Windows - FF/IE            - ctrl-alt-[key]