Android comes with an email app where you can have your combined inbox. The one that comes on the Motorola stock roms is the one with the red envelope. The other one is the one with the yellow envelope. With the latter, you can add exchange accounts and be able to have push email on Hotmail.
Then for gmail you have the option of using the native email app from Android (red or yellow) or use the gmail app. Which one is better in terms of push email and battery usage?
Same happens if you use a yahoo email account. You can use yahoo on the email app or you can use the new yahoo app. Which one is better in terms of push email and battery usage?