Sounds like you have most of your answers, but I use K-9 Mail and it's great. I use it to access my Gmail via IMAP (hate the built in Gmail app), my own domain IMAP emails and Hotmail via POP3.
POP3 works as expected, no problems at all. IMAP account set-up has an option to enable push email if your IMAP server supports it - Gmail and my hosting companies both do and my IMAP emails are delivered instantly. I've not seen any hit on battery life doing this.
Attachments - I have found that trying to open a .doc or .pdf file direct from the email causes errors but think this may be in QuickOffice, not K-9 Mail. All I do is save the attachment to SD and open from there instead.
Don't think there's an option to only download headers or limit size of email. Not noticed it in settings anywere.
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