The Live mail thingy is not too bad really. Windows 8, if you’re using touch, the built in Mail app is actually quite reasonable for basic on the go mail, and can access Exchange accounts.
Something more powerful, then Thunderbird. Though it lacks a lot compared to Outlook, mostly in the contacts and calendar department (and I think the calendar project plugin thing has been scrapped?).
Should all be able to do offline mail and send on connection.
Also, not sure but does GMail work as an offline app within Chrome (given it must work on Chromebooks)? Never tried, and obviously it’s tied to GMail mainly.