I'd definitely vote for mounted. Right now mine is on a separate rack and it works ok, but when I had one mounted on the exhaust fan above my regular stove, I loved it. And I hate to give up counter space. Having it more or less built in gives a cleaner look, and is so convenient. The mounting rig (don't know what to call it) also had a great light on it so my stove top work was great as well.
Oh, lord, didn't read the height thing. I'm tall as well; the microwave was at about face level for me. It worked well, but if I was 5' tall, it might have been a different story. And I hate bending down to lift or lower heavier things (heck, maybe that's why I don't bake!).