I also have an iPod touch 2G. The maximum iOS is 4.2.1. iTunes can get you there but you can have a very hard time finding compatable software for a 2G touch.
I wrote an app just for your type of problem,
Vintapps info/support: https://www.facebook.com/VintApps313
For a web based method see,
https://sites.google.com/site/appleclubfhs/support/advice-and-articles/finding-a pps-for-older-devices
Although I wrote my 99 cent app specifically to help solve this problem, I need to add that "I may receive some form of compensation, financial or otherwise, from my recommendation or link."
Once you update your device to the maximum, ios 4.2.1, you will have thousands of apps to choose from. They will definitively not be the latest greatest though.
Updating the device and passing the older model to another is still the best choice.