Hi Sherri,
You are pretty much bang on with the procedures for reinstalling Adagio to a new laptop or server. The basic steps are to install the programs using the most current CD you have, then check the website for any newer service packs. Also remember that all Adagio programs are contained on a single CD - you do not have to insert the precise CD that came with a particular product or upgrade - so it is most convenient to install from the newest CD not only for convenience but also to get as close as possible to the most current version.
A link to the service packs website page can be found here
Before you remove the original hard-drive, I would recommend re-printing the registration forms for every Adagio application, and also retrieve all License letters that Softrak has sent to you. This is so that after installing onto the new hard drive, you will have all the information you need to 're-register' and license the software. Your company information needs to be entered exactly as before, including capitalization and punctuation, otherwise the licensing won't work. In that case the software would have to be re-licensed.