Rob,
As a general rule, here is what I do when I upgrade:
1. Backup everything in your Username folder to another, temporary folder just in case you run into a problem.
2. Uninstall the T2 desktop and then install the T3 desktop. This shouldn't remove any of your data.
3. DON'T give your T3 a different username than your T2. None of your third party applications will be restored and any shareware that is keyed to you username won't be registered. Since the T2 and T3 have basically the same operating system, restoring from your T2 backup to your T3 shouldn't cause any major problems.
4. Once you've restored from your backup, you need to decide if you want to use the legacy PIM apps or the new T3 PIM apps. If you're using a third party PIM application like Agendus or DateBk5, you'll want to use the legacy apps and conduits. If you're using only the built-in PIM apps, you'll want to use the new apps and conduits. Take some time to read up on these and the differences between the two options in the PDF manual on the T3 CD. There will be particular issues with having to run both the legacy conduits and the new conduits if you want to sync both the T3 and the IIIc.
5. The only software issues you're likely to run into is getting updated versions that can use the larger screen of the T3 and the screen rotation feature. The PalmOne web site has some information on programs that have updates specifically for the T3. There are also threads here on software issues with the the T3 you should look over.
As far as the IIIc coexisting with the T3, the first thing you'll need will be a different user name for each. The problem is that that the IIIc uses serial drivers and serial port and the T3 uses USB drivers and a USB port. These can usually coexist but it's a matter of installing the drivers in the correct order. Usually, if you install the T3 desktop and drivers first, WinXP will recognize the IIIc when it's hooked up to the serial port and install the default drivers that come with Windows. If you're not using XP, it's a little more tricky. You'll have to install just the drivers for the IIIc (not the standard desktop install) and hope that doesn't disable the USB sync. If it does, you need to reinstall just the USB drivers for the T3 and that should allow both sets of drivers to work. The IIIc will sync with the T3 desktop but it won't be able to take advantage of the new PIM features like calendar categories and the additional contact fields.