Hi, Jeff,
I suggest that you keep iMovie 9 on your old computer and use it there if you want, but still learn iMovie 10 on your new computer. There will be a bit of a learning curve with iMovie 10 because it has a very different file structure and user interface than earlier versions. Once you familiarize youself with its features you may find that you like it. Here's a link to a good help menu/tutorial for iMovie 10:
http://help.apple.com/imovie/mac/10.1/
Whether iMovie 10 is "better" than earlier versions is a matter of opinion. The older versions have more features, actually. But as pointed out by others, they don't run very well on the new operating systems. So if you want to use iMovie 9 on your new computer from your iLife '11 install disk, you are going to be struggling with poor, and sometimes non-existent, performance. (You can still keep and use both iMovie 9 and iMovie 10 on your computer at the same time, though.) Your best bet, however, is to install iMovie 9 on your old computer and use iMovie 9 there when you want to edit a movie, if you don't want to use iMovie 10.
Do the same with iDVD. iDVD still works on High Sierra, but is becoming increasingly less functional with each iteration of the OS. You can still burn a DVD with an external burner, but the iDVD themes don't work properly on High Sierra. As the new operating systems evolve, pretty soon iDVD won't work at all on them. But you can still use it on your old computer. You can play the DVD on your computer or in a DVD player. Be aware that technology is moving away from DVDs, although I and many others still burn DVDs and enjoy working with them.
-- Rich