New Computer Setup and Transition from Old Computer

I have ordered a Dell XPS 420 that should be delivered tomorrow. I will be transitioning from my current Dell Dimension 4550 that I've had for several years, and I plan to have both my old and new computers running in parallel for a few days while I'm moving all the necessary data files to the new system and installing programs that I'll want to have on the new system. Because of the way my office is set up here in the house, I'll be able to have only one of the systems connected to the Internet at a time.
 
My initial thought is to keep the old system on the Internet at the beginning and set up the new system without being connected to the Internet. This will give me a chance to copy data files to the new computer and install programs. I assume that during the setup of the new system it will want to do some registering and updating operations from various websites - probably Dell, Microsoft and perhaps others. Will there be a problem if at first the Internet isn't available to perform such operations?
 
Once I've done as much as I can locally, then I'll switch the Internet connection from the old PC to the new one and continue with setup-related operations that require an Internet connection.
 
Does anyone see a problem with this plan? One advantage is that I'll be able to continue accessing the Internet and using email on the old system during the time that I might be having problems with the new system setup.

--Jim--