Well, don't mess with the family computer(bitter, bitter experience) The second system you mentioned would be a great Linux box, if you fancy it. New enough to bear up under decent load, old enough to be quite well supported indeed.
As for the laptop, it looks like it shouldn't be so bad.
http://theendlessnow.com/M70/m70-suse.html provides a quick runthrough of the install of Suse 9.3(by the chap who produced the pictures you linked to). If you keep the Dell restore disks on hand you cannot possibly go too far wrong, so it is always worth a shot(or dual boot, at any rate). Generally, one doesn't use Office, or WMP on a Linux desktop. You can use Crossover Office(a tweaked commercial version of WINE) to provide a compatibility layer that allows Office and some other popular productivity apps to run; but most people don't bother, as OpenOffice is free and quite decent for all but certain advanced functions.
In terms of install: Linux is highly customizable, it runs on everything from tiny embedded systems to supercomputers. This means that you, theoretically, have a huge amount of choice. In order to make things easier on the users, there are various distributions, some easier than others, some more feature filled than others, some that give the user much more choice than others, and so forth. Something like Suse is pretty streamlined. Pop in the CD, boot from it, make a few basic choices in the graphical installer, get dumped right into a nice desktop environment. Pretty much all the choices get made for you(though you can always change them later). Ubuntu is the same way; but it makes diffirent choices for you(e.g. GNOME instead of KDE as a window manager and APT as opposed to YAST as a package manager). In the middle are distros like Debian, which require more user imput, and aren't quite as immediately friendly; but give you more control. At the extreme end are distros like Gentoo and Linux From Scratch, where you build the entire OS and all the apps from the ground up. Massive control; but a bit of a headache for the first time user(and not something to do on a machine that you back up quickly).
Edit: I just noticed that fellow who put up that gallery has an email address listed. Linux users, especially the sort that build websites about their adventures, are not infrequently fairly nice about helping people out(and the flattery implied by emulation probably wouldn't hurt). Do consider dropping him a missive; but try his directions first, and google any problems you run into(google often knows quite a bit about linux issues) and he might well be happy to tell you about specifics of setup and so forth. He would probably be more useful than I for specific questions, as he has the machine in front of him, and I have something rather diffirent.
I do urge you to give it a go; but make sure that you have the restore disks available, so no matter how badly things get screwed up, and that can be a very useful part of the learning process, you'll be able to set them right without any trouble.
Additional edit: distrowatch.org is a good place to go for a look at the variety of options. Also, there are a fair few "What distro should I use?" threads floating around here that might prove useful.
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