We just did this with ours. We knocked our walls and kept the half wall as well and will have cabinets too. The standard size is 36". I'm pleased with the height of ours, plus we'll gain a few once the granite is installed.

Here is a link that might be useful: half wall

The above answer is correct, but you will have to look for specific stools for that height. Bar height can also be 42", which would take a standard bar stool.

There is no single "standard". Standard counter/bar heights are 30", 36", and 42" high...called "table-height", "counter-height", and "bar-height", respectively.

The most useful height, though, is counter-height. It gives you a large expanse of same-level workspace for large projects (baking, cooking, crafts, science fair, homework, wrapping gifts, etc.) as well as for buffets. [Total expanse depth = overhang depth + depth of counter over the cabinets on the other side, usually 25.5".]

For young children and older people, table-height is the easiest (and safest) height, bar-height, OTOH, is often difficult for both age groups to get in to/out of. Counter-height, I think, is the best compromise b/w the two.

Now, a related question...is there a reason you're keeping the half-wall? You don't need it for the counter support since you'll need corbels anyway. Half-walls are usually considered a waste of space if they're not needed. For example, if you have limited amount of room for an overhang, a half-wall (or knee-wall) takes up 4" or so of space that could be used for overhang.

What are the recommended minimum seating overhangs? Table-height (30" high): 18" overhang
Counter-height (36" high): 15" overhang
Bar-height (42" high): 12" overhang

Don't try to skimp on overhang b/c the people sitting at the counter will take up the same amount of room...they'll just have to sit further back from the counter edge if you have less than the recommended overhang...thereby taking up the same amount of room but not as comfortably. A human body can be squeezed just so much to fit a small space! (If your family is tall or has long legs, you might consider increasing the overhang from the minimums.)

One other thing...when planning seating, each seat will need 24" of linear space, regardless of counter height or overhang. This means a 48" wide breakfast bar will seat 2 people comfortably.