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road195 - others who use them should chime in. I have used a couple of different toe clips, Specialized, Christophe, Campagnolo, doesn't really matter. they come/came in three sizes, s/m/l.
Straps need to be leather to keep them from slipping in the "buckle." Nylon or plastic types, even woven, will slip.
That slotted plastic piece is called a cleat. They can still be found with a little searching if you want to use them. The whole configuration set is a bit challenging for riding on the road, or I should say commuting. Long distance is fine. It is the issue of removing your shoe.
As far as shoes go, look in C&V for threads on the topic. There are several and you can save a lot of time by finding them and then deciding what to do.
Personally, I use Look Keo on all my bikes, with one exception. The Colnago keeps the pedals, cage and straps. A lot less hassle from my point of view. I need to pay attention to the traffic scenarios while riding. I don't want to make a move with my foot and forget what I am wearing and how I am attached to the bike!
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