A core will contain a combination of each type to reduce chinking and twisting of the rope. A rope's flexibility affects how easy it is to handle and how easy it is to tie in knots. Some climbers prefer more flexible ropes, because they're easier to tie. But when loaded, those knots can become difficult to untie. Others prefer stiffer ropes because they're easier to thread through different climbing gear pieces and because knots tied in them are easier to get out.
Flexibility is largely a matter of personal preference.
Keep your rope clean. Dirt particles are extremely abrasive to ropes. Keep your rope off the ground at all times, and flake it out on a tarp when climbing. Avoid stepping on your rope, since doing so can drive dirt particles deeper into the rope surface. Be especially careful around your rope when wearing crampons.