@amirage:
Sorry, but your description sounds like this:
"I have my company's corporate offices in two different countries. So, I am thinking what type of car I should buy and how I should use it for a better fuel economy."
In any case, let me try to address your questions, if I understood them correctly. I assume that you don't actually need anything from that Google app functionality, but you are only talking about e-mail:
- Should I configure the account as an exchange using the native email app? I'm not bothered with syncing the tasks/ calendar/ contacts
- Should I configure this as IMAP Idle push?
- Should I just use the Gmail app
Basically, my query has to do with which of the above methods offers the best battery life and speed of push notification.
I have not seen any comprehensive comparisons of the battery usage for different mail apps and under different conditions. (There was some anecdotal evidence from somebody here that Aquamail has a lighter battery use, but it was just that.)
So, it would be hard to advise you on which of the three listed apps is best for you. I'd suspect that the actual differences (with exactly the same configurations) are miniscule, and you can safely choose based on other criteria such as privacy, convenience, functionality.
One would assume that Gmail app that uses their proprietary protocol for connecting to Google mail would have better handling of push notifications, - but my personal experience shows that it is not always the case: I've seen some serious hiccups there.
In any case, in Aquamail (or any other non-Gmail app), you want to use either regular IMAP type of account or "Google" account that uses OAUTH method of authentication with Google -- that choice is yours.
When you are asking for the fastest notification vs. the best battery life, - those are almost opposite to each other. You cannot achieve both simultaneously. You have to prioritize. Do you need the fastest notification (Do you really? Many users who say they do, when asked to pause and think about it, realize that 1-2, even 5 minutes do not really make any difference. But indeed, there are some
rare cases when a fast notification is needed.)
If you still think you do, - than choose PUSH.
If you don't need it to be immediate but want to optimize for the battery life, disable PUSH and set the synchronization frequency to the longest delay you can tolerate (5 min? 10 min? 15 min?), but not less than 5 min (otherwise you might as well choose PUSH).
Note that if you are expecting an urgent response, you can manually force Aquamail to synchronize your account(s) or a particular folder(s) as often as you want.
Hope this helps.
(Edited for typos)