It would be natural to think of a huge comet belt out beyond Pluto, somewhat similar to the asteroid belt between Mars and Jupiter, but this is not the case. If there were a single belt of comets they would always approach the Solar System in the same plane, but that is NOT the case. Instead, comets approach the solar system from all know directions, leading astronomers to believe there is a large 3-dimensional sphere of comets and asteroids which completely surrounds our solar system. It is much more like a cloud than a belt. For this reason comets come at us from all different directions.
Comets also follow different kinds of paths.
Some will make a single pass at the solar system and calculations of its path suggest it will not return. Others, like Halley's Comet have an elliptic-shaped orbit and visit us periodically, coming back again and again. Halley's Comet is perhaps the best known of the periodic visitors, returning every 76 years. Astronomers are not certain of the exact dimension of the Oort Cloud but mathematical calculations suggest that it may be 100,000 times further away than the distance between earth and sun. In other words, very, very far away.