Ugly corbels are the cheapest. Pretty corbels can be the most expensive. In between are steel and doing a post with stretcher bars. So much depends on the skill of the installer that you will be using that it would be best to discuss this with him during the design phase. Also remember that the back of cabinets are not load bearing and will need to be reinforced to be structural attachment points to carry weight.

and the cabinet needs to be firmly attached to the floor so it doesn't roll over.

Inexpensive corbels are the cheapest option but as noted above the cabinet structure much provide a sturdy mounting point.

Inset (i.e. buried in the underside of the stone) steel supports are nice because they can be made essentially invisible but they require a fabricator with the necessary expertise and also require adequate cabinet structure for support.

Depending on how much of the slab is supported by cabinets you may be able to do a 12" overhang without supports. There are fairly well established rules of thumb for how much unsupported overhang there can be. Typically if 2/3 of the slab is supported then 1/3 can be unsupported.
In you case if you have a standard 24" base cabinet then you should be able to do up to 12" unsupported. anything more would require corbels or hidden steel supports.

There has been quite a bit of discussion here.

Here is a link that might be useful: island overhang

In our case we are doing a 12" unsupported overhang (I despise corbels) on 24" base cabinets on a 72" length. Our fabricator refused to use the steel hidden supports because our island cabs are painted MDF.

MIA professional standards are no more than 10'' unsupported. I won't do over 9'' because I have seen usupported overhangs crack. There are a lot of stones coming to market that didn't used to because they were too fragile to transport. Resining and netting at the quarry was developed to be able to ship them, but they aren't all strong enough to even have a 6'' overhang. All stones are not all suited to the same standards, and it's alwys better to err on the side of caution than have a damaged floor or injured pet.

I agree with lwo.

Thanks everyone for you comments.

HerrDoktorProfessor, thanks for the link. Some good ideas.

Was also thinking maybe about possible doing a wood counter on the peninsula and granite on the L. It was nice when I did the kitchen 22 years ago, there weren't that many choices that there are now..

If you want to avoid the ugliness of corbels see the link below.
I really wanted to use these but out cabinet/countertop installer wouldn't warranty them. They would however, warranty an unsupported 12 inch overhang.

Go figure.

Here is a link that might be useful: Hidden brackets