The laser cutter should be your go-to for any kind of fabrication. If the laser cutter is able accomplish your goal then it is probably your best choice. The laser cutter specializes in cutting in 2 dimensions and should be used to cut acrylic, plywood(under .5" thick), MDF (under .5" thick), cardboard, and paper. It can also engrave any of the materials listed above, or aluminum.
Advantages - The laser cutter is the fastest way to fabricate something, it will take only a few minutes or even seconds to finish cutting. Also, as long as acrylic isn’t being forcefully bent, it will be more durable than using a 3D printer.
Disadvantages - While the laser cutter is very good at cutting in 2D, if you want to create something in 3D you’ll run into more difficulty. You can use multiple acrylic plates together in layers to create something in 3D, but generally it would be better to use a 3D printer.
As implied by the name, the 3D printer is best for 3D fabrication. While working in 2D the 3D printer won't be able to match the detail that the laser cutter allows, but for 3D fabrication the 3D printer will have far more depth than the laser cutter. If the laser cutter won’t work out for you then the 3D printer should be your second choice.
Advantages - The 3D printer should be able to create most models unless they have floating parts or other details that are impossible to print. The filament used is very durable and should withstand a moderate amount of force.
Disadvantages - The 3D printer takes much more time to fabricate than the laser cutter. 3D printing will often add support for any overhangs which will need to be removed after the print. 3D prints will become less accurate and miss some details with smaller prints.
Think of the CNC Router as a mix between the CNC Mill and Laser Cutter. It has the largest cut volume of any machine we have. It can also take material up to two inches thick. It is simpler than the CNC Mill, but isn't as robust. It can cut wood, plastic, Aluminum or Brass.
Advantages - The CNC mill can cut Aluminum. It is almost as accurate as the laser cutter and is less likely to melt plastic. It is easier to lean than the CNC Mill.
Disadvantages - Can't go very high on Z-axis (the mill goes a lot higher. Primary a 2.5D CNC Machine. The CNC Mill is better for 3D Machining.
This is the most difficult and least common way to fabricate something, however it will result in the highest quality fabrications. The CNC will use a high powered spindle to remove material and result in the finished product. The CNC works with nearly any material, including metal, and is incredibly accurate. However, this method takes much more time and knowledge which is why it should be your last choice of fabrication.
Advantages - The CNC mill can work with metal or nearly any other material. It is almost as accurate as the laser cutter and is less likely to melt plastic. It also can create 3D objects, but not if it has an overhang. If you learn how to use the CNC Mill you can flex on all of the other engineering students.
Disadvantages - Cutting metals is much more expensive than plastic. CNC milling is much more complex than laser cutting or 3D printing and takes significantly more time and effort. While using the CNC Mill, you will need to screw your material onto the mill so that it doesn’t move.