From your description, it doesn't sound like your tire was defective, just bad luck.
I doubt it is a defective tube. Usually defective tubes fail at the valve or fail by splitting along a seam. If it wasn't a pinch flat, that basically necessitates that it was a puncture flat. The other possibility is something sharp inside your rim not covered by the rim tape. Common puncture sources are glass, wire, and thorns. The cause of a puncture doesn't always stick around, especially if your tires have a thin tread. Whatever it was may have just poked through the tire into the tube and then fallen out. Wire can be really difficult to find if it only sticks through the tread by a fraction of a millimeter. Usually though, you will find something pointy inside your tire.
Patching a tube is pretty easy, just follow the directions on a patch kit. The important thing is to wait a few minutes to let the "glue" dry before applying a patch. It saves you a lot of money over buying a new tube every time you get a flat.
Flat's happen to everybody, and the heavier you are, the more often they happen, regardless of what kind of tires you use.
I haven't heard of skinny tires getting more flats than wider tires, but I haven't tried many wide tires. Common sense would suggest that skinny tires get fewer flats because they have less surface area to pick up debris, although higher pressure might make them more susceptible to what they do pick up maybe. The other trade off of wider tires is a cushier ride at the cost of more effort.