You don't need a character set for that. Disable smart quotes (Shift+Alt+Ctrl+apostrophe) and replace ' with ' and " with " (that's right: replace ' with itself, same for "). InDesign then dumbs down all quotation marks.
Manually dumb down curly quotes to straight ones -- Surely not?
The issue is a simple one at heart: the text file is already encoded as UTF-8, but there is something either in the file or in the application used to view it with that doesn't recognize this.
I've done a couple eBooks in InDesign and haven't had this problem at all.
What version of InDesign are you using? Are you using default export settings? What does the output look like in Adobe Digital Editions?
I just did a quick test that included "it's" in a few paragraphs, and it looks line in Adobe Digital Editions, and in the HTML when I open it in TextWrangler.
I concur -- TextWrangler is UTF-8 aware, and I've succesfully edited InDesign's ePub output with this. It might be as simple as the OP's editor is not UTF-8 aware.