Laser for cutting styropor

Hello!

Few months ago I build my first CNC machine.
I've made some tests:
- carving some text in wood and plexi

My last test was to plot on Styropor. The result was awesome.

Now, I would like to cut out my drawing.
Well, I know how to do it with hot wire technique (but this is not an option here -> wire has to go through Styropor plate)

I got an idea to use laser.

Here is the problem.
I figure it out that 2 types of lasers are used on CNC machines (CO2 laser and laser diode).
I believe CO2 lasers are more powerful, but have shorter lifetime.
I watched some youtube videos and saw what different lasers can do, but I still don't know in what direction should I look.

So. What will be laser used for:
- to cut 25mm styropor
- engrave text to wood, plexi
- if possible cut 5mm plexi

What type of laser should I use?
And what is the recommended power?

Links, suggestions,... are very appreciated

Thanks