They used to call those things "half-clips"--sort of a toeclip without the strap--meant, I think, to be used by people who were a little hesitant to go the whole clips-and-straps route, and I think they were also popular with roadies moving over to MTBs back when clipless pedals weren't so well-known/mainly used by the pros.

Anyway, I still use toeclips, and I find that my feet are happier with what used to be called a touring shoe--not sure what they call it now. It has a stiffer sole than your average sneaker or running shoe, and that stiff sole transmits more of the power from your legs into the pedal = stronger pedaling. A bonus of many such shoes is that they can be converted to shoes for clipless pedals simply by adding a cleat on the bottom of the outsole. Look for shoes that are advertised as "SPD compatible." I'm contemplating making the move to clipless any day now--well, at least when I get my new bike out of layaway.