How you cleat it depends on how you route your mainsheet, and there are lots of possibilities. Cleats (either cams or clams) have fairly narrow working angles, so you usually need something down at deck level (a block or fairlead) to take the mainsheet as it comes down from the boom and route it to the cleats.
My favorite system is to deaden (secure) the mainsheet aft (to the aft deck, gunwales, a rope traveler, etc.) then run it up to a block fairly far aft on the boom, then along under the boom to a second boom block just behind the mast. From there, the sheet leads down to deck level, through a block attached to the lower mast or mast thwart and aft to the sailor. An open clam cleat (has no built-in fairlead) on either side of the leeboard thwart can be used to cleat it. See drawing below.
The major advantage to this system in that the forward boom block forms a very effective automatic downhaul, flattening the sail when mainsheet tension is high and easing it for more draft as sheet tension decreases. It will work well on just about any sail that has a gooseneck or boom jaws that are free to slide up and down the mast. Either cams or clams can be used, but if you buy camcleats, make sure they are ball-bearing models (Harken, Ronstan, etc.). The non-ball-bearing cams have a tendency to jam at precicely the wrong time and you can't get the damned sheet free to ease the sail out and save your bacon. In general, Clamcleats are just as effective for this use and easier to deal with.
Yes, the aft end of the boom is usually higher, but on old Old Towns, often not by a lot. The higher tail end allows the boom (and the sail's clew corner) to have a bit more clearance above the water as the boat heels and the sail is let out to the side. One of the most common capsize scenarios for lateen sails happens when a big puff of wind hits and the sailor eases the sail out to de-power. If the boat is heeling and the sail's clew corner hits the water, the corner will plane along on the surface, preventing any further easing. At that point, if the wind pressure is greater than the sailor's leverage as he hikes out (or doesn't) then the boat rolls over. A little upward angle aft on the boom helps to build in some safety margin to prevent this (so do really tight abs and the ability to hold the boat flat through a puff).
It's been so long since I saw one of the stock brackets that I don't remember how it was oriented. Somebody will know.