I have been using toe clips and straps for 40 years. I tried various cleats and clipless systems (e.g., Look, Speedplay Frogs) and never liked them much. I have wide feet which doesn't help matters.

A few years ago I started using MKS Touring pedals with toe clips (with Shimano touring shoes), but I've started seeing more people using platform pedals with and without pins. Pins seem to make sense but you can gash your shin or tear your tights with them. I recently bought MKS Lambda pedals after watching Mat Ryder ride the Great Divide Mountain Bike Route and a transam from Astoria to New York City on them. 

A big advantage is I can wear any kind of shoe or sandal with Lambdas. Also, during winter I often put some sort of boots over my shoes. No problems with getting my feet in the toe clips. 

(I have to say that one of my pet peeves is riders who use clipless pedals during mass events like the Ride for Your Life yesterday in DC. Over and over, I had to stop while a rider in front of me missed the clip in and had to start over. )

And, by the way, Mat's video series about those tours are fantastic.

I have Shimano M324 pedals on all our bikes. This pedal has SPD on on side and flat on the other so that I can ride with ordinary shoes if necessary. I have Shimano brand MTB shoes.

On the tandem Mary has a M324 pedal on one side but a flat pedal on her dismount side so she does not have to worry about unclipping.