To create a Clean Install (formerly known as Erase & Install) of Mac OS X 10.6 Snow Leopard (the 29 USD Upgrade DVD is a fully working retail version of Mac OS X and does not need a prior installation of Mac OS X on the Mac), follow one of the following guides:
Short version: Clean Install of OS X 10.6 Snow Leopard
Long version: Mac OS X v10.6 Snow Leopard: How to Erase and Install
OR
Use CarbonCopyCloner or SuperDuper to make a 1:1 copy of the old HDD to the new (properly formatted) HDD in an external USB enclosure for 2.5" S-ATA HDD, then do the switch.
OR look at any of the already available guides out there.
If you want to keep everything the same, what would be a good idea is to put the new hdd in a USB enclosure and copy the drive with Carbon Copy Cloner. Then just swap drives after you're done.