To have all my emails downloaded and stored locally i need to use pop3. I also want to have the benefits of IMAP and PUSH email so i instantly get my messages on my phone. The following settings are the best.

• setup email in outlook with pop3, with the setting leave on server for 14 days
• setup all the required emails on the phone via IMAP using K-9 Mail (or GMAIL for the inbuilt Google account)
• when setting up the IMAP accounts on the Android phone with K-9 use the PUSH email option
• setup all shared pop3 accounts up as IMAP in outlook aswell. This is so sent items can be copied into outlooks sent folder if required

These settings give the best of both worlds and cover me if Googles servers go down, and i can use my own email accounts with PUSH email.