If I wanted to do 10" deep, 2" thick, ~24" wide floating shelves, where the shelf consisted of a box that had a dado for LED strip lighting, what would be the best approach?

The shelves would be holding dishes, glassware, possibly small appliances, possibly 750ml bottles of liquid. 

I have access to the studs in the wall behind (I'll be framing it), so my first thought was a buried bracket of some kind. 

French cleats seem like there would be too much leverage at the front of the shelf unless I made them substantially thicker.

The rebar in the stud idea has appeal, but the shelf won't be solid, so I'm not sure exactly how i would do that.  Maybe some inner structure designed to slip over the rebar?

Thanks,
Adam

Sounds like your shelves are going to be carrying more weight, but I built my wife a couple of shelves that are maple 3/4" thick by 9 1/2" wide. Used 1/2" Spax lag screws driven into the studs, then cut the ends off with a portable band saw. I was going to figure out a way to affix the now studs into the shelf, but they required a rubber mallet to gently seat them (I don't hit things with my hands anymore). They are solid and going nowhere. Would I start putting really heavy stuff on them? Nope! But as book shelves they are working great.

Take a look at the Ikea floating shelves for how they mount. That is where I got the idea for the ones I made, but simplified it, using just lags.

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So if I wanted some ultra heavy duty shelves and had access to the back of studs, I would start welding up some brackets. Possibly using scrap 1/2"-3/4" pipe (Not rebar) welded to a 1/4" plate 3"x6" pre-drilled with holes. Put a hole in the drywall, then insert the mount and put one bolt into the bracket. Level on the other side and continue bolting it into place. The second mount will take a little more setup time, as it must be leveled on two planes.

As to the shelf I would make the mounting area solid, and either use a router to cut half circles in each part and glue them together, or attempt to drill them straight. I would think the router would be more accurate, just gotta have the right bit. 

Another option for less than what the poster above showed is to buy Ikea shelves, and use just the brackets. I believe Home Depot sells them too. They are around $10 per shelf.

Sounds like your shelves are going to be carrying more weight, but I built my wife a couple of shelves that are maple 3/4" thick by 9 1/2" wide. Used 1/2" Spax lag screws driven into the studs, then cut the ends off with a portable band saw. I was going to figure out a way to affix the now studs into the shelf, but they required a rubber mallet to gently seat them (I don't hit things with my hands anymore). They are solid and going nowhere. Would I start putting really heavy stuff on them? Nope! But as book shelves they are working great.
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So if I wanted some ultra heavy duty shelves and had access to the back of studs, I would start welding up some brackets. Possibly using scrap 1/2"-3/4" pipe (Not rebar) welded to a 1/4" plate 3"x6" pre-drilled with holes. Put a hole in the drywall, then insert the mount and put one bolt into the bracket. Level on the other side and continue bolting it into place. The second mount will take a little more setup time, as it must be leveled on two planes.

As to the shelf I would make the mounting area solid, and either use a router to cut half circles in each part and glue them together, or attempt to drill them straight. I would think the router would be more accurate, just gotta have the right bit. 

Another option for less than what the poster above showed is to buy Ikea shelves, and use just the brackets. I believe Home Depot sells them too. They are around $10 per shelf.

Sounds like 1/2" lag bolts might be sufficient

What do you think about 12" lengths of 1/2" iron or galvanized pipe, sunk into the stud 3.5" and then attached to the inside of a built up shelf via some pipe straps and lateral blocks? 

Or would I just be better off with something like these: http://www.aandmhardware.com/?

Thanks,

Adam