I don't want to get involved in scripting just yet.
Yes, I remember making that mistake.
Scripting sounds scary and difficult: it's not, it's a piece of piss. For example, making cutscenes with camera scripts is actually much easier (and produces infinitely better results) than using triggers. Head over to the Editors Depot and read the following tutorials:
Johan Gustafsson's scripting guide
snYpir's Friendly Intro to Code Snippets
snYpir's Camera script tutorial
messiah's camera.sqs tutorial
That's a lot of reading in one go, so break it up with the Tutorial Mission: it's a working mission with examples of everything you need to know to make a good basic mission. It has a couple of simple camera scripts. Remember that you are already using scripting language. All a script file does is make the stuff (that could go in a trigger) easier to read.
Returning to the triggers question, you now basically know all there is to know about controlling triggers. It's all down to using variables as switches. You can use any virtually any name you like for your variables, just avoid things that could be words or commands. Don't use a variable "trigger", use "trigger1".
If you wanted a sequence of triggers to fire in order (I beg you, don't use this to make a trigger based cutscene, use a camera script) all you need is a sequence of variables:-
trigger1
Activation: as you like
Condition: as you like
On activation: trig1=true; whatever else you want
trigger2
Condition: this and trig1
On activation: trig2=true; etc
and so on ad infinitum.