I started with Slack running on a P1 90MHz with 16MB RAM, which ran but was VERY slow.
I have since experienced Slack running on a PentiumMMX 166MHz with 64MB RAM, Pentium 230MHz with 64MB RAM, 128MB RAM and 256 MB RAM as well as P4 3.2GHz with 1GB RAM.

Without question the single biggest contribution to speed is the amount of RAM.

Faster hard disks help, but low memory causes incessant disk usage as memory is swapped in and out.

In general I find Slack running KDE on older hardware is slow compared with Win98 or other Windows OS, but the comparison is not fair in that Linux is a true multitasking operating system, whereas Windows is designed as a single user operating system. With a fast machine the differences fade to negligble.

KDE is definitely a drain on sytem resources. Other window managers will give increased performance on older machines. Still, it is good to learn how to use KDE apps within KDE before attempting to use them within other window managers. In general I find the corresponding X apps run faster than KDE apps.

Congratulations on getting an installation on a 1.7GB drive. I would have considered 3GB to be a bare minimum, and even this leaves little space for downloading and installing upgrade packages.

Another contributor to performance is the graphics card. If you can live with the lesser quality, a simple card with an efficient driver can be a lot faster than a more capable card.

As for questions on LaTeX:
Kile uses KDE libraries, too.
If you want something akin to Kile, use TeXmaker.
Also, if you are short on resources, you could consider LyX or TeXmacs.
LaTeX is best learned with the assistance of the Not so short Introduction to LaTeX (link to .pdf).
As for Firefox, well - it is not long ago that FF was a low-requirement program. Nowadays, it is getting heavy.
I would go with Abiword, too. Be aware that Abiword wants to compile with Gnome libraries, but you can use GTK2, too - and less Gnome libs.
As for using Slack on low-end computers: I am using it on an old 600 MHz, 160 MB RAM laptop. I upgraded from 32 MB - it made a huge difference! Also, after recompiling the kernel, it speeds it up.