M424 don't really allow normal shoes. I had a set of M525s (the same but with a metal cage) and the cleat stands proud of the cage quite a bit. 

You can buy [single sided pedals](http://www.evanscycles.com/products/shimano/a530-touring-pedals-oe--ec050912)* that will let you ride in flats on one side of the pedal and let you clip in on the other. As for shoes, something like the [Specialized Tahoe](http://www.specialized.com/us/en/ftr/shoes/recreational-fitness-shoes/tahoe)? They're supposed to be wearable as normal shoes.

*I'm not sure if this is what you meant by half clips, but in case you meant toe-clips, don't do it.