Mark, your grandson sure has talent!
I have several jewelers saws, and buy blades by the gross once a year. I get them from Rio Grande jewelry supply.
Although I have a few #8 (largest) blades, and a few #0-5 (smallest), I generally stick with a #0-2 for fine stuff, and #3 for thicker material.
ALWAYS install the blade so as to cut on the "pull" stroke. This lets you have more control of where you are going with the saw. And tighten it as said above, get that little musical note. And after a bit of sawing, tighten it again, as the blade will "stretch" just a bit.
For most work I use my 5" Knew Concept sawframe. This allows you to tighten the blade a bit while it is still in the work, a big benefit when cutting inside a perimeter. The 5" part, by the way, is the clearance between the blade and the back of the saw frame. They come from 3" to, I believe, 8" for the throat depth. All the blades are 5.5" in length.
Cut into a block of beeswax or "Bur Life" from Rio, this will lube the blade for you. The Bur Life is a great lube for drill bits also.