Yup, looks like a Dory is the thing for you. Rigid raiders are the most well known Dories available, but many boats use that type of hull, including fishing craft. On a lake it is perfect because of the shallow draught, and as people said, it takes a load of abuse and can be driven straight up the beach.
Er, well, yes, but they cost a fortune. And for lake use it's just a teensy bit of overkill

I can't imagine you'd stay at full speed for long even if you reached it - not to mention the weight of them!! Twin 150s are not for carrying, whether two or four stroke, let alone how they affect the boat's handling (nose up flips spring to mind).
Abbe I'd recommend a 50hp outboard. Four stroke if you can afford it is better, because it's quieter, cleaner, more efficient and goes wrong less, although they are heavier and more expensive, and trickier to repair if they do break down. You could get 75hp or 100hp if you can afford it. Depends what you're using it for - for general purpose use 30 is enough, although I wouldn't use it as a rescue boat for canoeing/sailing as it wouldn't be quick or agile enough.
There was a man I met in the US who had twin electric 20s on a small Dory, which he charged with solar power. He said they were really reliable, surprisingly quick, silent, and cost nothing to run. Of course you pay a lot for them in the short term, and in winter I imagine it might be a problem charging it (although you could use the mains), but certainly something to look into. Only trouble with twins is it means hydraulic steering gear and a wheel, rather than hand control. The boat you buy may already have this though.
Best of luck in your search
