I too have a DS II, a short-shaft will "work" if clamped directly to the transom as O'DAY intended, although you will need to shim it a bit to get a better angle for the mounting. I started out using a short-shaft outboard (2.3 hp JOHNSON) and as I say it will work.....but is not ideal! O'DAY recommends a long-shaft and before buying my DS II I really doubted the need for the long-shaft. I now have a 2001 4HP Johnson with a long-shaft, it was worth the slight extra cost!! I would definitely go with a long-shaft (20") on the DS II especially if I might keep the outboard to use on my next (most likely bigger boat). I no longer have trouble with the prop coming out of hte water in waves, and can move around the boat with out risking the prop coming out of the water. I'l linclude a picture of my boat and motor, I did end up adding a plywood motorboard, bolted to the transom to try to better angle the outboard. I don't like the look of a bracket, especially those adjustable ones that lift the outboard, they look out of place on a low-freeboard boat like the DS II. A fixed bracket is OK, but I prefer what I have.
As for size, on the DS II I wouldn't go with anything bigger than 4-5 hp, unless you intend to get that bigger boat after only a year or two with the DS II, 4HP is plenty of power (could go with smaller, but the 4 provides a great reserve of oomph!) A 2-3 hp will be about right...but then may be too small for your next boat. Over 4hp tends to get heavy as well, the Honda 5 is not too heavy, but is still more than the 38# of my 4hp Johnson. Unfortunately, the newer 4-strokes are not lightweights, but the Mercury/Tohatsu/Nissan/Johnson 3.5 hp is not bad, I think it weighs about the same as my 4hp Johnson. Not sure if it offers the option of a remote tank, but that is a good feature....especially once you move up to a bigger boat where you may be using the motor more and will appreciate not having to hang out over the transom to refuel the built-in tank on the outboard.
Finally, consider the Torquedo electric outboards. Not cheap, but they are supposed to be good sailboat pushers and shaft length is adjustable on some models I think.
PS: I added an afterdeck to my DS II, so...that is why in the pictures she may look more like a DS I. Unfortunately, I don't have any pics showing the old short-shaft outboard up close while hauled out.