I did something similar a few years ago as my first built-in project.
What I found helped was using glue as well as hardware to attach the framework to the wall, and tying them into more than one side of the alcove. Structurally they were some strips with a plywood box built around them and some nice facing on the front.
Tools were really just a tenon saw for the frame pieces and a bandsaw for the back of the plywood where it's scribed into the uneven wall, but you could use a hand coping saw for that just as well.
Diall 8mm universal wall plugs, 7 per shelf (3 on the back and 2 each side)
(The framework doesn't span the whole way cos I was trying to save money and just use one piece of lumber per shelf, probs a false economy)
Good luck!
Spent a drizzly lunchtime there yesterday, weird seeing it on here!