What's wrong with the standard mail function on your phone? I have both Hotmail and Gmail icons on my Lumia. But then again, I don't use any other fancy features in gmail.... as long as I can open and then delete the mail, I'm fine. lol
I was using standard mail function in windows phone by adding my gmail account to that. When I'm using my email i would like to write, read, reply and delete my mails(i hope these are not 'fancy'). Not just read and delete. Standard mail feature in WP doesn't sync all folders or labels at once. If you are in inbox and give 'sync' command it syncs only inbox, not drafts. I faced a situation when i needed to access my drafts folder for emergency i realized its not synced yet and it was taking too much time(even though i had just 3 drafts). I know it can depend on my network speed too. But, my good old Asha 200 with a Series 40 OS had better standard pushmail capabilities than windows phone. Don't get me wrong, i'm love Lumia. But this is a drawback(for me). Still it does not sync my draft folder!!
Another thing is if there is a new mail alert in notification bar you can tap it to read it. Once you are inside the mail there is no way to go to inbox from there. If you press 'back' arrow it goes to the start screen. If you check the 'more'(...) menu, there is no option for that. You have to go to start menu and access the mail tile again!!! Which is just one more tap but annoying. I mean that's not i want to use my mail.
Currently i have started using metro mail and i like it. You get all the standard features of an email.