I think the commenters here have summed it up pretty well. You have to gain experience to find out what you, specifically, prefer. Me, I tend to lean toward the smaller blades when possible. The #2/0, #0 and #1 are usually what is affixed to my saw rather it be spiral or straight. My preferred brand is Pegas. If I'm cutting fretwork on a piece that is dimensional (straight lines, circles, etc) I prefer a straight blade. If it is a line that is critical and could make or break a piece, I'll use a skip or double skip blade which cuts a little slower, in my opinion, than a MGT blade which is what I normally use. For portraits that are erratic (various sizes cuts, random locations) I'll us a spiral. I can't give you any preferences towards puzzles, segmentations, etc, because I haven't cut those. The more professionals here at the Village will have to comment on those.
I'm usually cutting 1/4-inch ply that is stacked, 2-layers. I have cut 3/4 and even 1 1/4 material. The only issue I had was with the 1 1/4 material where the blade deflection from pushing the material into the blade. The top of the material where the pattern was located was true to the pattern. However, the bottom of the material was cut off and broke through some of the thinner frets because of the bending of the blade.
Good luck on your quest!