Hi, and welcome to the org.
Besides a DVD drive (no need for a burner), I'd say go ahead and download the AMV.app you can find down in the video section, because all the tools it contains other than the premiere plugin are useful tools for all sorts of video editing programs.
What I would do to ge the most out of an older, slower computer is follow all the steps in
this guide, as far as getting an avs file, but then load the avs into virtual dub (part of the amv.app pack), and convert the clips you want to use to high quality mjpeg, then edit using those clips.
mjpeg is fast, which is good for slower processors, and the clip files will be only about half the size of YUV format huffyuv, using quality setting 19 in the picvideo mjpeg codec.
You can download the picvideo mjpeg codec for free from
www.jpg.com, but it will put one of those watermarks on your video until you pay the $18 to register it. You can still use it for free to get a feel for the editing process, though.
There are definitely cheaper alternatives to Premiere out there, and some (many?) have downloadable trial versions that expire after awhile. (even premiere has a 30 day demo you can download.
I've heard of Majix music maker, vegas video, goldwave, and there are probably others.