This seems the best way to me. When I moved from PC to Mac, I copied the music from one to the other using a USB drive. The way to do it is to copy the folder structure from the first machine to the USB drive and then import it into iTunes on the other. I forget the correct terms but there are two ways of doing that. One requires the USB drive to remain visible and reads it from that and the other actually copies the music files to the new hard drive. The latter of course is the one you want here.
You also have to authorise the second machine, which is not a problem as you are allowed 5 at once. If you are getting rid of the first machine remember to deauthorise it first. I made that mistake once when I reformatted my hard drive and again when I put a new hard disk in my laptop - leaving me with 2 machines which were authorised but no longer available. Eventually I had to deauthorise them all and then authorise just the current machines. That went smoothly and worked fine, although I was a bit nervous of leaving myself with no working machines.
Good luck.