What size batten for breakfast bar

Hi
Adding a breakfast bar to our kitchen. Worktop is 38mm thick. What size batten should I fix to the wall for the breakfast bar to rest on? It will be supported with 1 or 2 legs as well (opposite side to the wall).

Thanks

use 2"x 1" for the back support screw to wall at approx 12" intervals
i always run a bead of no nails along the wood before fixing to wall (belt and braces )
then use screws at a 45 degree angle to secure worktop to wood

45° angle? please explain..
do you mean sideways as surely it's impossible to angle back to front as te wall prevents the drill going that way, and going front to back kind of defeats the object as you wouldn't even touch the worktop

what's wrong with using angle brackets screwed to the batten and worktop to secure it?

assuming your tiling or are happy to have a 6mm bead off silicon

use some angle iron[steel /aluminium /stainless]drill a hole every 150-200mm to screw into the wall in the area the worktop will cover
remember the holes you drill to go into the worktop will be on the outside face
you will have to chamfer the bottom edge to sit in the curve on the metal

this way theres no more than the 6mm protruding with no ugly brackets blocks or battons showing unless you drop your to worktop height