Hi Mel.
If I were you, I'd start with a book from MobileRead (they're free!) and try putting that on your Reader first.
Download any epub or .lrf book from the E-Books tab in the blue bar near the top of the MobileRead page - remember where it is downloaded to on your computer.
Then, start Calibre and click on Add Books (top left). This will bring up a normal Explorer dialogue where you can navigate to the book you downloaded and click on Open. The book will then be placed in your Calibre library. Then, connect your Reader to your computer. After a few seconds, Calibre will detect the reader and you will be able to move the book from the Calibre library to your reader by clicking on the Send to Device button. After disconnecting the Reader, it will then be on the list of books avalable on the Reader.
Hope this helps

If you have any issues with using Calibre I'd suggest you take a look at the Calibre Forum on MobileRead. Lots of people who know way more than I do about Calibre on there (like, say, the people that are writing it).
With regard to your second query about changing PC's, I'm really not sure; Calibre won't care, but I'm not sure about ADE. Which is why I suggest you start with a free book first.
Hope you enjoy your reader as much as I'm enjoying mine!