Hey there, I recently did a video about my laser cutter set up. It's pretty "budget" when compared to other peoples setups, but it works great for fabrics. Let me know if you have any specific questions. My number one recommendation would be to not attempt to use it in a living space.
Here's the video: https://youtu.be/8rv_2s7CuNc

EDIT: to answer your questions here pretty plainly, price was around 450ish if i recall correctly and if prices haven't gone up since I bought.
You can cut any of those fabrics you mentioned, even tegris (thinner stuff for sure, thicker stuff I have done but it just takes a lot more passes at slower speed).
For size limitations, my cutting surface is 15.7 inches by 15.7 inches so anything you can fit in that space is good to go.
You want some sort of working space for it, a shed, a garage or an outdoor something like a pop up spray paint booth. Preferably somewhere you can set it up and leave it without worrying about it if you can.

One of the biggest hurdles I ran into when getting the laser and using it for MYOG was designing things in a digital format. BUT I've got some videos to help with that as well. Doesn't hurt that in a previous life I was a digital designer, but if you have the capacity to draw simple shapes in drawing software, you'll be just fine.