It depends on what kind of puzzle you are making.
For a jigsaw puzzle, FD has special (really thin) blades just for that purpose.
If it is a 3D type puzzle (which if you are using 3/4" material it probably is) Your favorite 3/4" cutting blade will do just fine.
If you are making a simple child's jigsaw puzzle you can use a thicker blade for a wider kef for ease of assembly for smaller folks.
No, the wood won't burn at slower speeds and yes, it does make it easier to follow the pattern lines at slower speeds. Burning comes from heat generated by faster speed of the blade AND build up of saw dust in the cut AND of course a dull blade gets hotter too.
Yes the packing tape will help lubricate the blade and reduce heat as you are cutting so, it is generally recommended for almost any type of cutting by most folks.
I will add that slower speed of course increases the time it takes to cut a pattern. As you gain experience you will find that you want to go to a faster speed. You will also find that sometimes when making a long straight or curved cut it is easier to follow the line by going faster.
Another thing I will add just for information. If you do get off line as you are cutting, DONT PANIC just ease back to the line and keep going. After you remove the pattern you will never know where you may have gotten off line and neither will anyone else. Sometimes if you get off line and stop and try to correct too fast, it will be more noticeable than if you had just continued the cut.
HAVE FUN AND KEEP MAKING SAWDUST!
Rog