If you can dry fit everything nicely with no bumps or chunks in the way, then you should be relatively good to go. I'd repair this with hide glue myself, but using some good wood glue would work too. Hide glue is preferable because it's easily undo-able and it shrinks as it dries, so under clamping pressure, it will actually suck the joins closed even tighter.
Martin is (of course) right that as long as the inner lining is still in good shape you should still be able to repair it pretty well.
If there are cracks visible on the surface after gluing from missing shards of wood, the best repair method is to razor out a triangular shaped sliver (wide on the guitar surface, narrow in the crack) carefully cutting right along the grain line. It is triangular shaped on the cross-section. This way when you glue in a new piece of spruce, it will fit right into the grain and when scraped and smoothed, should blend nearly invisibly into the top. If there is a cross-grain scratch or chip though, these are much more difficult to repair invisibly.
When the top is glued down, there will likely still be loose braces inside (the lower two braces look like they would have been knocked loose from the pics). The best way to assess this is to reach gently in through the soundhole and feel them. Anything that is loose will need to be re-glued to prevent noise/buzzing and keep the top integrity in good shape.
I've successfully gotten digital cameras into the soundhole and taken some pretty good pics of the interior using the timer on the camera. If you can get pics, they will tell you much more, otherwise, you can probably get an inspection mirror and a lightsource in there to help determine the problems, if any.
Cleats are a great repair, but I would use them only if I could not re-glue the braces inside (or if there is significant damage inside, but it's not worth removing the top). IMHO, the best is just re-gluing the braces back to where they are supposed to go. Again, hide glue is preferred because of the shrink factor, but it is also brittle and can't gap-fill worth a damn, so it needs to be used cautiously when things fit really tightly. You'll need a scissor jack to help support the braces in place while they glue, or get some creative clamping and bracing in place if you don't have access to a scissor jack.
Take your time and document the process so others can learn from it. The good news is that if you stick to classical strings, the likelihood of a successful repair is increased. This would be a bit more challenging on an acoustic guitar since the top integrity is more crucial for dealing with the higher tension.
Good luck, this looks like fun...
