"I've read that this only minimizes the app and doesnt completely close it. And this could eat some of your battery."
The Mail, Safari and iPod apps that come with the Touch will be running in the background after they are launched the first time after powering up the Touch. After using any of these 3 apps, hold down the Home button until they exit to stop them from running in the background. These apps are optimized for background operation so I don't believe they significantly affect battery life. They do use memory however. Turning off WiFi, Push and Location Services (and exiting any running app) will help with battery life when in standby.
None of the apps in the app store are allowed to run in the background so you only need the long Home button press if they hang.
The SysStats Lite app displays the memory usage status and current running status of these apps and other processes.
http://appshopper.com/utilities/sysstats-lite