Here's a tip from another user that may help you:
"I was running into the same problem trying to find apps for my daughters Iphone 3g running 4.2.1. What I did was go to the Itunes store through Itunes on my PC, and then went to the bottom of the main page and clicked "Browse." On the browse page I selected, App Store, Games (category), Kids (subcategory), and then a list of apps appears below.
I sorted by date (oldest to newest) by right-clicking next to "price" and choosing "release date" on the menu that pops up. The date created field will then be showing, which you can click on to sort newest to oldest or oldest to newest. I downloaded a bunch of free apps starting from the oldest (by name - you don't have much else to go on). Of the 30 or so I added to my Itunes, about 27 of them were compatible with 4.2.1.
This is defintely not a perfect way of finding apps, but after spending a lot of time searching for a better way this was the best I could come up with."
While it specifically mentions iOS 4.2.1, it should apply to iOS 3.1.3 as well. Other posters may provide other tips on how to look for compatible apps.
Regards.