All my bikes run old-school pedals with clips and straps, and for most riding I wear a pair of Shimano SPD-compatible shoes but with no cleats (for the stiffness). For touring usually I'll wear a pair of trekking/hiking shoes with a GoreTex liner instead.

Pedals I like and use include the SunTour XC-Pro (no longer made, and going for stupidly high prices on Ebay), MKS Urban Platform (one-sided, but with a nice, flat, supportive platform perfect for long rides), Velo Orange Touring Pedals (very light, nicely made, and supportive), and SR Low Fat MTP-126/127/129 pedals (similar design to the XC Pro, but not as high-end and still available at good prices on Ebay).

For clips I prefer the types shown in photos above by other posters, nylon with a two-part strap carrier (which is probably what the OP meant instead of a double strap setup, which is something racers used to use back in the pre-clipless days).

I wouldn't be too keen on the pedals shown by the OP, as they are more for racing/road biking than touring. The edges will start to dig in, especially on lightweight or running shoes, and they don't have much support.