Take a look at the "AptonCD" package, in the "universe" repository.

Looks like it's tailor-made for this situation (which I'll be in,
myself, shortly - including dial-up...)

You can use it to make a CD containing the packages from your
/var/cache/apt/archives/. , which can then either be copied into the
same folder on the new machine, or mounted as a software source.

It won't do everything. For example, if you have the Adobe Flash
Player (nonfree), AptonCD will copy the installer - but the Flash
Player itself will have to be downloaded again from Adobe when the
installer runs.