To more easily find compatible apps:
iOSSearch - search the iTunes store for compatible apps.
Apple Club - filter apps by iOS version.
Starting when iOS 7 was released, Apple now allows downloading the last compatible version of some apps (iOS 4.2.1 and later only)
App Store: Downloading Older Versions of Apps on iOS - Apple Club
App Store: Install the latest compatible version of an app
You first have to download the non-compatible version on your computer. Then when you try to purchase the version on your iPod you will be offered a compatible version if one exists.
Also do you really have a 3G iPod? A 3G can go as high as 5.1.1 while the 2G can only go as high as 4.2.1. They looking identical on the outside
Identifying iPod models
iPod touch (3rd generation) features a 3.5-inch (diagonal) widescreen multi-touch display and 32 GB or 64 GB flash drive. You can browse the web with Safari and watch YouTube videos with Wi-Fi. You can also search, preview, and buy songs from the iTunes Wi-Fi Music Store on iPod touch.
The iPod touch (3rd generation) can be distinguished from iPod touch (2nd generation) by looking at the back of the device. In the text below the engraving, look for the model number. iPod touch (2nd generation) is model A1288, and iPod touch (3rd generation) is model A1318.