The procedure outlined in that article essentially amounts to changing your DNS settings to point your domain at the EC2 instance, and running Nginx (a webserver) on that EC2 instance, with it proxying requests to Google Apps. This general idea can be applied to almost any AMI. I would recommend using the 32-bit version of Amazon's Linux AMI (ami-7f418316) for the purpose (it works in the free tier, and is optimized for good performance. It is based on RHEL/CentOS, so you would would change the following lines:
sudo apt-get update
sudo apt-get upgrade
sudo apt-get install nginx
sudo yum update
sudo yum install nginx
The remaining instructions remain essentially the same (although, I don't believe the 'sites-available' is created by default, and the main nginx config file is in /etc/nginx/nginx.conf).
As an aside, if you use the AWS console to launch your instances, you will note a yellow star beside instances that are eligible for use in the free tier. Any of them should work fine for this purpose, although, the simplest ones (i.e. ones that have not been pre-loaded with an assortment of unnecessary software) would be the best suited to your purpose.
If you do wish to stick with an Ubuntu AMI, you can find the official list at Ubuntu's EC2 Starters Guide. This lists ami-f333fe9a as the current Ubuntu 10.10 32-bit AMI (which is eligible for the free tier), although, you may prefer to use 32-bit Ubuntu 11.04 instead (ami-e358958a).