You can get entry level hobby laser cutters from around $400 and up. The light ower output ratings of lasers are often misstated in W (Watts), but are in fact mW (milliwatts - 1/1000 of a Watt). For example, Laser pointers are considered quite hazardous over 1mW and are regulated at 5mW maximum. That's the kind of thing those idiots are shining at aircraft and blinding pilots with. A 1W output laser is an extremely powerful laser and very expensive, we are talking industrial. It is difficult to figure out the true laser power output of some of the machines on the market and I suspect some of them list the input power requirements, which could include the controller and motors, etc. So you would need to carefully research any machines you are interested in. The important things are thickness, materials and speed of cutting or engraving, along with accuracy and repeatability whih should not be a big deal for your purposes. But be careful about those numbers, because the same mchine that can cut 1/4 of soft wood may not touch metal and even the type of wood and metals makes a difference. There are a large number of them. What materials and thincknesses you can cut (or engrave) depends on the power out put (light power) of the Laser, the focused size of the beam (smaller is better as it concentrates the energy) and the cutting speed. It's not linear scale for power, if all else is equal. Engraving obviously takes less power then cutting. You can also make several passes. But some of the lower end machines can manage wood up to 1/4 (depending on the density of the wood) and thin metals. You can also get rotory attachments for some machine so you can engrave or cut round objects as well as flat stock. You will see machines with the same power at widely varying prices, but the difference is going to be quality, robustness, and accuracy - including repeatability. You are not making interchangeable watch parts, so you don't need extreme accuracy and repeatability. File input types can be very simple and most machines handle many type. They usually do TIFF, JPEG, DWG (a common CAD format), etc. plus some more mainstream CNC formats. Simple Software for design and CNC output can also be obtained very inexpensively. But don't ask me for recommendations on either machines or software. I have been retired for a number of years and out of the loop, plus I was more into CAD/CAM and 3D printing and in engineering management than hands on for the latter years of my career.
