Hi, Bill. Good questions. The biggest recipe for disaster for shelves is not putting a hardwood strip across the front of a shelf to make an L shape. 3/4" BC plywood is good and commonly used but without the support of a hardwood strip, sagging is almost inevitable. Particle board, chip board or flake board are just not good quality for this kind of application.
For diagonally bracing your cabinet, there is nothing better than 1/4" plywood bradded into the back, except 3/4" plywood. It would be nice if you could route a rabbitt out in the back to make the plywood fit flush but not really necessary. 3/4" or 7/8" brads about every 6 inches will hold it square for a long time even without the rabbitt.
Again, rabbitts for the shelves are nice and will make the cabinet last longer but not really necessary. Four 1-5/8" drywall screws across the sides will hold the shelves for a long time as long as you have the hardwood strip in front to make the L shape and putting the brads thru the plywood back into the shelves will help also. Be sure that you drill and countersink holes for the screws, including the ones that hole the hardwood shelf on.
Again, a table saw is nice to do the cutting of the plywood but if you don't have one, a circular saw will work if your measure very precisely and cut to a straight edge guide. A good fit is critical and that starts with good cuts and good measuring.
Now for the bottom line. I just bought a sheet of 3/4" plywood and paid about $28 for it. Design your shelves and calculate the cost. Then go to the unfinished furniture store and see if you can find a unit that will fit your needs. You should have a pretty good idea of what is needed from a design and construction standpoint and you can make a logical decision.
Don't even think about a bookshelf made of partical board with a picture of wood glued over it. I had a computer desk (came with the computer) made that way and one day I ended up with a lapfull of computer. The guarantee was absolutely worthless.
Good luck and let us know how this comes out. Henry in MI