As far as I've ever noticed, that's exactly how it's supposed to work--when you start typing, it hides the pointer so it's not in your way as you type, and it reappears instantly as soon as you touch the mouse/trackpad. I don't think there's a way to change this, although I've never heard of anybody complain about it before.
I've never seen it take a while to appear, though--sure you're not just having trouble finding it when you start moving it around?
For reference, it's actually right where you left it--if you click without touching the trackpad it will register the click properly, although the pointer stays hidden until it moves at least a hair. Maybe you have "Ignore accidental trackpad input" checked in the Trackpad control panel, so it's taking a second to register after you put your finger on it?