I have had the same issues with the iPad 1 and iTunes and have tried everything listed here with little success. I adjusted all the setting in Safari, erased everything and restored from backup, and even erased everything and didn't restore from backup. I even reset my iPad 1 to its factory settings using iTunes on my mac, which is quit drastic. When I asked an apples sales rep in the store she said she had the same problem, that after browsing in iTunes, the app will always crash after some time.
I believe the cause is low memory. Every time it happens in Settings>General Settings> Diagnostic & Usage > Diagnostic & Usage Data
I get a list of crashes and it says something like
LowMemory-2012-07-02-175903.plist
Basically LowMemory is the problem and then the rest is the date and time since I know that these are the exact times when it crashes.
What is interesting is that my mom just got an iPad 3 and of course it does not have this problem. I believe that it is because the iPad 3 has 1 Gb of ram where as the iPad 1 has only 256 mb of ram. Unfortunately Apple has made the iTunes app require to much ram to run properly. I believe that it really needs a minimum of 512 to work for longer periods of time. It is a fundamental problem that apple could solve if they would tone down the graphics in iTunes.
Solutions I have found are the following.
Close all other apps. This can help a little.
Restart the iPad. This will give you a longer period of time but iTunes will crash inevitably.
Reset the iPad by holding down the home button and the power button for about 15 sec. This will give you the longest browsing time before a crash.
I am also on my second iPad 1, since the first one had dust under the glass.
Things that I tried that may or may not of had an effect: Do the settings listed above for Safari, reset the iPad and use iCloud to restore your data, or do a hard reset which is delete everything and don't restore the data (which really ***** because you have to restore everything manually and backup everything methodically on your computer). The hard reset where you don't use the iCloud backup is because an apple sales rep told me if it is a software issue it may be transmitted through the back up in the cloud. I tried these things and am not sure I could tell a difference.
I am curious if anyone has an iPad 1 that does not do this? Please let me know.