First, realize that, among other things, your old drive will not work in the new 360 Slim, so you would need to find one of the old models in order to keep your harddrive. If you do happen upon the old design, the second thing you should realize is that a lot of the downloaded content on your harddrive is keyed to your current console. There are ways around it, but it isn't as straight forward as plugging your old harddrive into your new console. Note that this method should also work with the new slim models.
As for the differences between the 4GB and 250GB models, the 4GB model is pretty analogous to the old Arcade models. It comes with an empty harddrive bay, which accepts the same style harddrive as the 250GB model. Some games may not allow all of the features for the 4GB consoles, although this may have been fixed. As far as I know, the rest of the hardware is the same. You could just buy the harddrive to put in a 4GB console, but that's paying an unnecessary premium. Personally, I would get the 250GB slim model if I were forced to replace my console at my cost.