We have Gmail for our office email and I route some of our email through our test servers. I've been running a setup similar to yours for a while but eventually plan to drop Gmail completely.
Google give you the first steps here:
Once you have google set up to rely email to your postfix server it's a simple matter of setting up postfix to handle the sendoff.
You'll need to create your accounts locally. This will take easy password control/updates away from your users unless you install postfixadmin. This might not even be an issue for you if you're only interested in relying email through this server.
You can get away with a config file as short as this:
sudo nano /etc/postfix/main.cf
myhostname = mail.somesite.com
mydestination = $myhostname
myorigin = $myhostname
mynetworks = locallhost
relay_domains = $mynetworks
This is the basic set up for delivery of email from gmail through your server and out to the recipient. Note that you need to set up a PTR record for your domain and IP. Otherwise other server's may reject your email.
Google will also let you set this up for individual accounts so that you can test with yours or a test account before setting the whole company up.
This setup does not cover receiving email. If someone replies to your emails you'll want to be sure that your mx records continue to point at gmails servers so you can check your email there.
Tail your mail log files. They'll help you make your final adjustments
tail -f /var/log/mail.log
Send an email from the gmail app and watch the logs in real time. They're pretty easy to read and very informative.