I'd hazard a guess here that this is a hell of a project for a virgin to take on...
Others may stop by and correct me, but...
* You can insert each DVD into your laptop (I assume it has a DVD drive?)
* You then need to rip each DVD to your hard drive (something like CloneDVD or DVD Shrink - I can't remember which of those, if either, can defeat copy protection - which would certainly be an issue).
* You then need to find a way of converting all the DVD (e.g. .vob files) to an 'editable' format such as .avi or .mpg. If you're using Windows Movie Maker, I think it'll have to be .avi. There are plenty of utilities out there - just do a Google search - but few of them are, IIRC, freeware - it'll probably cost you about $25.
* You then need to edit the resulting file into the length you want.
* Repeat the above for every DVD.
* Now, you have twenty edited files, probably all in .avi format.
* At this stage, what I would probably do would be to gather together all those .avi files into a single project, separating each one with a chapter marker.
* Then, I'd find myself a DVD authoring program (WMM won't do this for you - but again, there are plenty of DVD authoring programs out there that are a whole lot cheaper than Adobe Encore...) and author a DVD with a menu/buttons that would allow you to select each individual track, or play them beginning to end.
* Then I'd burn the DVD.
Given the process I've outlined above, you need neither firewire nor fancy hardware.
I may have misunderstood the requirement, and others may be able to think of a quicker/easier way of doing what you're after (I have a talent for making simple/quick jobs into difficult/long jobs) - but, like I said, from my perspective, if you've never done even any basic video editing before, this would be a hell of a baptism by fire... Good luck!
Premiere Pro, Encore, Photoshop, Ulead VS6, WXP Pro, Core 2 Duo, 2GB, 2 x 250GB SATA3 drives, 2 x 250GB USB 2 external drive, DVD writer, GeForce 7300 GS 256MB
The biggest fool can ask questions that the wisest man cannot answer...