I think the only countertops to be wary of using would be marble or tile with white grouting. Granite, quartz, Corian, or even formica should not give you any trouble with staining.

quartz corean white synthetic marble any one as per your budget

normally the breakfast counter height varies from 36" to 42" if you want it to be perfect height select the stools for the counter first then check the height of the stool and add 12" to 15' in the height. distance between the stool seat and table top should be 12" to 15" max...

In that case , wall hung cabinet would be able to support the slab and sink. Is there a reason you want it it to be wall hung cabinet. You have made safe skirting space and even a floor mounted cabinet should be fine here. Regarding material, for the carcass you can opt for granite vertical slabs and BWP ply shutters for floor mounted one. But if you prefer a wall hung cabinet then a BWP ply carcass sould be good enough. The wall groove should be cut only on the longer side. Thanks, Nitin Cornerstone Designs, Bangalore