I know that there is a way to update your iPhone 3G, but my phone is getting more and more slow. So if it’s possible to get the old version of the apps, I could avoid the risk of making my phone even slower when installing the update.
Around September 17, 2013, Apple began letting users download the "last compatible version" of apps which were compatible with iOS 4.2.1. This doesn't work for all apps, and it doesn't permit downloads of versions below iOS 4. Search for apps on your iPhone or iPod (not on your PC).
Here's an article describing the change:
You can locally transfer apps by version, such as when you sync your iPhone with iTunes, but finding the old versions of many apps is really not possible. If you're running iOS 5 or 6 (I forget if the 3G got the update) then this might cause incompatibility anyway.
I'd recommend upgrading your device if you use a lot of iOS apps. You don't necessarily need the latest and greatest, though I'd recommend an iPhone 4S or later to last you a few years (better still, an iPhone 5). The 3G is very old now, and hasn't been officially supported in software updates for a while.
You can assume that the OS is only sole responsible for your phone running slowly.It would be better that you use your phone with only apps that you use the most.
There are other ways(risky) in which you can make your phone run in normally.This can be done by downgrading to lower version of OS,which you won't like to do.
iTunes will always offer the latest versions