You *should* use the package manager in Slackware, and I would recommend it above anything else. However, the package manager included with Slackware is much simpler (and very different) than the Debian package manager. It does not resolve dependencies and cannot be set up to automatically download packages. The best way (in my opinion only, of course) to install applications in Slackware is to compile applications and create Slackware packages that can be installed with Slackware's package manager (`installpkg packagename` should do the trick).
I have posted several times about this and won't type it out again (check this post
, for example), but I prefer either writing SlackBuilds manually (see here
) or using SlackBuilds from slackbuilds.org (or, to a lesser extent, slacky.eu). You can also try gnashley's src2pkg if you want, which I haven't tried but has been extremely highly rated from basically everyone that has used it (I haven't seen a negative review yet). It attempts to automatically compile applications and create a Slackware package that you can install (but you can also pass parameters to the application as well if you want to customize it).
Using Slackware's package manager together with Slackware packages makes it easy to install, upgrade and remove packages. If you just perform a blind `./configure; make; make install`, it could be difficult to upgrade or remove the application, and it makes it difficult to track which files on your system are from which packages. If you use the package manager, almost all of your files can be traced to one package based on the listings in /var/log/packages. It's very convenient.