Are you using NTFS Partitions? If so, yeah, copying the 20GB partition isnt a bad way to go,
i suggesst you create a seperate partition for your Page File, as it is faster, and if your keeping your 20GB HDD in the computer, put your page file on that drive.
I would just burn your data to CD, and reinstall everything on the new drive, everything will run better.
The transfer shouldnt take long, HDDs are very fast for data transfer. It might take an hour or two, its gonna be slower than normal, because its going to copy it Byte for Byte.