For burning .isos to CD or DVD on Windows I use ImgBurn, it's free, easy to use, and never let me down.
http://www.imgburn.com/

Going on the list of goals:

Given that the modem is probably a winmodem (not necessarily so), I doubt you'll manage this. I tried this ages ago as well; back in the slackware 3.x / 4.x days, and winmodems just would not work... Too bad. The workaround is getting drivers and recompile them. Not something I would suggest for a new Linux user nowadays.

This worked back then, and still does. Ethernet cards got detected fine. This was the easy part ;-)

Unlikely that this will work. Wireless is something that only got supported somehwere late in the 2.4 kernels if my memory is anything worth relying on.

If you do a full Slack installation, X comes along. In 4.0 it was still not very easy to set it up, althugh some setup scripts worked pretty fine. 10.x and later should help you out much better. 12.2 is still the way to go, in fact; I am currently running Slack -current on a Pentium2 with only 64megs of memory, obviously I refrain from running X. (More
memory incoming for that, just to make the machine work)
12.2 will give you better tools to setup and configure your system in a more easy manner, I expect 13.0 to make your life even easier.

Not sure how this would perform, but OpenOffice.org sounds like the program to use for this, as -afaik- it is one of the few programs that can somewhat read and write Word and Excel files.

That you say "Slackware was made to be flexible"; that much is true, but flexible and able to do everything is two different things ;-) Back in the days of 4.0 the world looked much different, people ran windows 3.11, 95 and maybe a few already 98; Look at how desktops look nowadays, the world has changed beyond recognition. What Linux was capable of back then and right now has drastically changed as well. Use it to your advantage.

Slackware is known to be the most reliable and stable distribution with each release. ( -current does not count as such, that's for those who like to cut their fingers on the bleeding edge!) 12.2 is very stable and allows for some practical maintenance tools I missed in prior versions (aka slackpkg) Don't hesitate to run the latest release, the kernel only got better as did almost all the stuff Pat put into Slackware. I wonder why you would choose to do a fresh install of an old version. Sometimes people do that for "good old time"-'s sake. Especially if you're new, I'd go with the latest release (12.2 in this case, it's been out for some time and was stable from day 1. Patches are available on the mirrors and easily installable with slackpkg)

The images, as said are bootable; I think it would mess things up if you tell Roxio to "manipulate" the image. It should just take the image and put it on disk, no questions asked :-) The slackbook (on www.slackware.com) should help you a long way on the run; But feel free to ask questions any time.

I didn't catch where the modem was initially identified, but I DID read up there somewhere that it is maybe a Lucent modem. I have had good success using the Martian driver packages for the Lucent modem in my laptop, but again, as mentioned many a time already, these drivers may not be available or compile on that old Slack. They do work for kernels=2.4 and =2.6 though.

Also, another burning program not many people usually mention, is 'InfraRecord' which is a free program for WinXP (and maybe others) which is very easy, literally a two-click operation to burn an ISO image to a disc. Worked great for me in the day..

Cheers,
Sasha