Deborah, you do beautiful work!
I've done similar work with the laser, but mine is an older machine, low
power and an aging laser tube that needs replacement, so it takes forever. (probably not compared to what you're doing!)
But.. having said that, if you are considering a machine purchase to do this kind of work, you'd likely want to look into a galvo laser, rather than a gantry system. (which is likely what most of us have)
The gantry laser moves a head back and forth like an inkjet printer does.
The laser beam is positioned by mirrors, so wherever the head is, the
beam is pointing straight down from the head. This head moves at high speed, back and forth .. back and forth and gradually moving from top to bottom or bottom to top. That's the engraving mode.
In the cutting mode, it works from a vector file and the beam moves along the lines in the file. In your case you would use a vector program (like CorelDraw, for instance) to create your files, which would be a series of cutting lines. Once sent to the laser, the head will follow those lines and cut the paper.
But the galvo laser works differently. The head is stationary, but the mirrors move at high speed. For the type of work you are doing, this is more commonly used than the gantry system.
There are drawbacks to this. While the galvo laser will cut these much faster than the gantry will, (seconds vs. minutes) the work area is smaller, since the mirrors can only move so far and keep the beam in focus. The work area may be 4,5 or 6 inches, for instance.. while a gantry laser may have a work area of 18x24 or 36x48 inches, and the head can cover all of that area.
Cost is also a factor, and time = money. You can charge more for work that takes longer because it is intricate. You can't get away with charging more because you have a slower laser!
My suggestion for now would be to check out some YouTube videos on laser cutting and engraving. Make some notes, watch the speeds and see what they're engraving and how it works. I would do that before checking prices.. you don't want to base your purchase on the price, rather base it on what your actual needs are. (then shop price!)