That's what I was thinking of using, is maple veneer plywood, and router the edges all fancy.
Plywood won't hold a shaped edge. Even if you're okay with the layers of ply showing, when you try to shape the edge, you'll end up with chipping, leaving voids in the layers of ply. The best you can do, if you're intent on molding the plywood, is to apply a uniform finish with wood filler and sand it smooth. It's challenging to achieve a clean look this way on a rounded edge, and nearly impossible on a complex profile. Painting is mandatory.
Better is to apply some sort of solid wood fascia. It sounds like you want to keep it simple, so I wouldn't groove or spline on the fascia. Just get some pre-fab wood molding strips of the same thickness as your plywood, tack it on with finishing nails (drill pilot holes to avoid delamination and bulging), and then use wood filler to fill the nail holes and cover the seam. Plan on painting, not staining.
The real challenge is your desire for this to last several years. Without superior joinery, you're going to end up with a carcase that racks, even if you build in gussets and fasten the back to all sides. It may be quite sturdy at first, but after a couple years of minute movement from usage and bumps, it will become flimsy, especially if you ever move it. This is the nature of the all-plywood carcase. You can't dovetail plywood, so you can
- extend the sides above the top and below the bottom, allowing the top and bottom to be dadoed in;
- use thick (7/8" or 1") plywood, with rabbet-and-dado corner joints, and at least one fixed shelf glued into dados; or
- build the carcase from framed panels consisting of solid wood rails and stiles, and plywood panels.
The last option is by far the best, gives you lots of options for strong corner joints, and eliminates the problem of the appearance of the plywood edges (though, not for the shelves).
Don't get your advice on woodworking from YouTube. There are a number of excellent books (none of which are sold at Barnes & Noble) on basic woodworking skills that are inexpensive. Find recommendations at dedicated woodworking sites. If you must watch videos, then look nowhere but
here.
Finally, don't expect much from an all-plywood bookcase. If you don't invest in materials and joinery, you'll reinvest in a new bookcase in a few years.