Well, I've done this some times now, and last time in june/july on my nightshift. Since you are unfamiliar with slackware, and linux generaly it's hard to know what packages you will need. If you have no clue on mechanics and you are going to build a car from scratch, what do you buy in the hardware store?
(Disclaimer, this is how i did it).
Basically you will need all packages in the A series. That would be in the slackware/a/ folder on your slackware cd1/dvd. You can actually drop several packages, but I'm guessing you can save perhaps 10-20MB. At least not very much, so I wouldn't bother with that in the beginning. So in the slackware installer, choose to select packages from A (And drop the rest, AP/D/E/L..) and install all packages in A.
After the installation you boot your shiny new system into slackware, and now the installation REALLY starts. Now you walk trough the folders, starting with AP, and upwards. You would want something to edit textfiles, so you will perhaps take nano/joe/jed. One or all of those. I prefer nano. (All those in addition to vim of course :P).
And you essentially work your way trough the folders and install all packages you need. And this is why its hard for us to say what you need, be cause you need what you like. And we don't know what you like. There are 5 (or something) different text editors. Several different audio-players, different cd-players, different window managers etc. Thats why a full installation is so large. It got multiple programs for the same task.
But use your system, when you discover that "Hey, I need <insert something useful>". You install this from your cds/dvd. In some time, you will have a minimal working system. This will of course go a _lot_ faster for those how have used slackware for a while and know what they need. Generally you need some basic tools in the command line, Xorg, sound system, network etc.
When you install software from packages and try to start them, you will eventually get something like "Missing library libXev.so" (An example. Its wrong, so don't bother pointing it out :P). Now, what do you do? Well, you can google. Ask here, or (preferably), you can have a copy of /log/packages/* of a full installation in your system. This folder contains a file for every package on your system. This file contains a path to every file included in that particular package. So you can search through these files and locate what package containing libXev.so. (Thats why you need this folder from a full installation, because your minimal system only got information on what YOUR installation have).
Then you continue. One package might require several packages. And one of these package might have dependency issues them selfs. Hence gnashleys comment that it could take months before you have a working minimal system just the way you like it.
When you finally get it working like you want to, it would be a shame to do it all over again, therefore you use alienBOBs tagfile script. This generates files containing information about what packages in the A-folder you have installed, and in AP, D, L, KDE,... you get the point. So next time you are doing an installation, you locate these tagfiles, and the slackware installer reads them and installed exactly the same packages that you had in the previous installation. (Except third party software that isn't included in the DVD).
"That's how the cookie crumble". You can only learn by using slackware, this takes time, but it will probably be worth while if you really intend to stick with slack
Well, this was a long post. Much longer then I intended. Hopefully you wont get to confused about it. :P
