Help setting up email system

Hi,
I have just bought a domain name and hosting. I want all my mail forwarded to my gmail account and then i want to be able to send emails from my gmail account as my domain name.

I am able to set this up so it sort of works but when i send an email it comes up on another computer as being sent on behalf of Domain@domain.com.

I want it to come up as just my new domain name. If that makes sense.

Also as i am not in the office for most of the day i was hopping their was away to hook all this in through my iphone as well