Don't use pine wood!
That is, unless you like turpentine flavoured lamb
Other than watching the hangi at the Moot last year, I have only tried it once, that was with a rabbit in clay, left with the fur on and not so much smeared in clay as folded into a clay "pitta pocket", over which a fire was lit, useing up to 2"x12" sticks, then allowed to burn down over an hour or so. The meat was steamed and very tender. Using hardwood is important I think.
As for heating stones, I am sure that some are better than others, but you can't always be picky, beyond not getting those that are wet (in the tide zone, or river bed) or those that are glassy like flint or quartz.
Hope it goes well!