What are the differences between "clincher" and "tubular" tires?
If you want simple and easy to fix then you sure as heck don't want tubulars.  

Someone else will probably provide more details and links, but clinchers are rims/wheels with a tube, then a tire is mounted over the tube and the bead of the tire is hooked under a lip on the rim.

Tubular rims have no lip.  The tire encases the tube completely and is sewn in typically.  SO fixing a flat means cutting open the tire and patching the tube, then sewing it back up.

The tire assembly is glued to the rim.

Heat from brakes can melt the glue supposedly and cause tires to roll off. 

The rolling resistance used to be much better on tubulars.  Unless you are a purist or a pro I don't think there is a reason to go with tubulars these days.