According to one source, the tooth pitch is the distance on the circumference of the gear for one tooth and one gap. If your value is correct, you'll have quite a large diameter gear.
On the other hand, if you are referring to pitch diameter, that brings the gears down to almost a tiny level.
If you consider the 1750 rpm of the source, a destination rpm of 40 would mean a 35:1 ratio, a nice integer ratio.
If your starting point is a 25 mm drive gear, the driven gear will be almost a meter in diameter (875 mm). Obviously, if you go larger with the drive gear, the driven gear has to go up.
A compound gear arrangement may be a bit better suited if you have the vertical space to stack gears. Another possible option would be to create and use a planetary gear set. 35:1 is well within the capabilities of such a mechanism.
There are "bunches" of planetary gear models on Thingiverse for 3D printing.
I'm currently working on a project involving a much lower ratio, only 1.5:1 which means an 80T sun gear and a 120T ring gear. Planet gear sizes are meaningless in this application. In order to get the greater reduction you require, you would have to stack at least two stages and that gets out of my current range of understanding.
Thingiverse has a few multi-stage designs, one that looks particularly attractive. The design is based on a 6:1 reduction, therefore two stages would provide for 36:1, nearly the aforementioned 35:1.
The output of this design is not shown, but the crank drive could be adapted to take a motor shaft. If you desire to construct this of plywood, you could take the tooth counts for the components and enter them into one of the many gear generator programs available.
The above linked site shows how to accomplish a greater reduction with a compound gear set rather than a planetary gear set, but will still allow you to construct the necessary drawings (and downloads) to build a model.
If I did this properly, the above site and the link provided will appear with a 1750 rpm input and a 36 rpm output. A bit lower than you requested, but I had to change only one figure and the result is suitable for demonstration purposes.
To attempt to answer your primary question, fewer gears means less wear, less noise, but much more space used to accomplish this. Planetary gear sets are not known for being quiet, especially when input is so high, but a compound gear set may not be much quieter, although there will be fewer gear components in the latter design.
Design for the largest size you can fit to your application, to spread wear out over a greater area. Lubrication, even on wood, will be of great value at the speed you've provided.
Larger gears will be in the range of hand tools such as a coping saw, unless you have the great resources of a laser cutter. I think I'd have had great fun in your class if I had such opportunities in my youth.