How do I set up a wiring closet that connects to the exterior of the house?
Your local hardware store should have a selection of conduit that's suitable. Generally any PVC should be OK as it's designed to survive the weather, and does so very well. I used 15mm, but I wasn't running coax - just data cables. An SC fiber connector would not fit through a 15mm conduit, so you'll either have to get a larger conduit than this or get it crimped after it's been through the hole. Go for the larger conduit - it'll be cheaper and easier.

Penetrating the exterior wall depends on what kind of structure your house is built with. Ours is double-brick exterior, so I just drilled through it with a 15mm masonry drillbit and a large hammer-drill. Concrete should be pretty much the same. If you don't have access to a hammer drill, every few seconds stop the drill and pull it back a few cm, then start again. Depending on the thickness of your wall the drill bit will get incredibly hot, so be careful after you've made your hole.

With the exterior conduit, if it's PVC then it should be pretty safe against the weather as it is. If you need to run outdoor connectors outside of the conduit, then IP65 or 67-rated devices should do well.