The guys walking funny were wearing SPD-SL cleats, which are compatible with the pedals above but not what you are looking for I assume.
I have these Gore-tex boots called
Shimano MW81 though I was luck and paid only £80 for mine from the same shop. Because they are gore-tex they should be waterproof and I did choose them because the reviews were good. The shoe is nice and stiff apart from the ankle cuff which is soft so that you can flex it.
For pedals I have these so I can wear regular shoes if I want to -
http://www.wiggle.co.uk/shimano-a530-spd-single-sided-touring-pedals/
but you could get this if you only wanted to wear the cycling shoes -
http://www.rutlandcycling.com/6245/Shimano-M520-MTB-SPD-Pedals.html