Generally bigger is stronger, but in the case of REO mesh the size needs to be in proportion to the thickeness of the concrete and the use, in this case 6 mm is plenty strong enough.

BRC is readily available in many of the construction hardware stores. They are all over the place.

Get the ones that have closer spacing. The A series usually space the reinforcement 200mm apart and the B series closer at 100mm. Not that the A series is not adequate, but the closer spacing B series can help to reduce cracking of your counter top concrete.

Also, you mentioned that the top is 12 feet long. I assume that is the distance between supports beneath the counter top. I would suggest you get your contractor to drill some holes in the wall along the 'long' side of the counter and install some bars coming out of the wall to overlap with the reinforcement in your counter top. This will help provide further support to your top and also reduce the probability of cracks at the junction between your counter top and wall in the future.

If you really cannot get the BRCs, they should also sell R6 reinforcement bars. These are 6mm diameter round bars that is used quite commonly to make the rectangular reinforcement (we call it shear links) for concrete columns and beams. You can get this and ask your contractor to cut and assemble the mesh on the counter top himself. This is actually better because you can cut the bars to suit the shape of your sink opening etc, whereas BRC mesh come in standard pattern and size and will result in more wastage.

Hope this helps.

I would go for 6mm and make the rebar spacing smaller... 

Provided the wall is also a rebar concrete if only red brick it will not stay long, even faster if its cement brick.