How can I save my web access login on the iPod Touch?
This is included by Apple in the latest iOS. You want to list that network as Auto-Login in the preferences for that network.

When you are in range, you first have to go to the Wi-Fi Networks sheet in Settings.app, Press the white > with the blue circle and set your preferences for each network:


Auto-Login controls whether the log in credentials are saved, so turn that on. You don't need to enable auto-join, but it will reduce the taps to re-join this saved network if the device sleeps or is really out of range. 

Turning on Auto-Login makes the device attempt to load www.apple.com and watches as you enter the wifi credentials needed for whatever web site is used to join the wifi network. Many open public sites are automated so don't worry if it sets itself up without prompting you at this point.