Okay i try to help
But i'm not the linux crack in fact. The Problem with Linux is, every Distribution handels stuff a bit different and i haven't seen slackware in action so far.
I try to explain what i have understood so far.
Linux uses several Running States e.g. u can define State 1 Load Programm A&B, State 2 Load A&B&C to make it a bit abstract. In 99% of the case we talk about Runlevel 2 or 3, where 2 is mostly multiuser Linux system and 3 multiuser Linuxsystem with X Desktop/Server.
In you're case first of all find out which "runlevel" your system is currently. An easy way should be typing "runlevel" on the shell prompt. The Answer should look like "N 2" or "N 3", at least it does on my debian system.
After u have found out the runlevel u know where to edit. The Configuration for each runlevel is being held in directory's which are created according to the run level.
e.g. in my distribution the config dir for rl 2 is /etc/rc2.d and for rl 3 it's /etc/rc3.d. In you're case it should be very similiar.
If u have a look into the directory u see a lot of so called soft symbolic linksc which are comparable to a shortcut in Windows but being much more sophisticated to use.
The symlinks u see, all have a name starting with a letter and a number. e.g "S20ssh -> ../init.d/ssh" or "K10ssh -> ../init.d/ssh2"
The Letter S means start and the lette K means Kill which is similiar to stop

The numbers are like priority's. First ist starts 10 then 20 then 30 etc etc. The Kill process is top down, meaning it kills 30 then 20 then 10 etc etc.
What u actually have to do, to get you're script being called every time the system is booted. Is to make a symlink to the script which could looke like this
"S20tsserver -> ../init.d/minimal_startscript"
"K30tsserver -> ../init.d/minimal_startscript"
The command u have to use for creating symlinks is "ln". If you're script minimal script would reside in /usr/local/tss2/minimal_script, the syntax for creating a ln inside rc2.d would looke e.g. like this.
"ln -s /usr/loca/tss/minimal_script S20tssserver" &
"ln -s /usr/loca/tss/minimal_script K30tssserver"
Double check that u always use the option -s, otherwise you created a hardlink. Which means that if you delete the link, the original file get's deleted as well !
If everything worked out well, the server should be started at boottime. But of course u have to experiment and read a bit to get working the first time.
This is as good as i can explain so far, there maybe other or even easier methods of doing this but then u have to wait for a real linux crack.
Greetings
ScOp3