For the ideal way to run ozone safely, you need to have an ozonizer, an ORP controller, an ozone reactor/skimmer to run the ozone through, and carbon at any location where water and/or air discharges from the skimmer. Most people run ozone through their skimmer. Ideally you would have a second skimmer/ozone reactor to run your ozone with since the ozone impedes skimmate production. Not all skimmers can handle ozone so your skimmer doesn't have an ozone fitting, you should find out from your skimmer's manufacturer if it is safe to run ozone through your skimmer and what the best way to do it would be. People that have used ozone for a while know how to detect when too much ozone is being added into the tank and what amount of ozone is required for their setup and they may be able to get by without an ORP controller if they are primarily using ozone to obtain clear water.
As to weather a UV sterilizer is a cheaper alternative, as stated UV killed both good & bad bacteria along with free floating algae the passes through it. An ozonizer oxidizes the water which also kills bacteria, along with breaking down fish waste from within your tank. Because it is breaking down the fish waste, it does make your skimmer pull out less skimmate ,but (if it is like mine) your skimmate will be raunchiest smelling skimmate that you've ever been around. IMO, ozone is better than UV, but UV is used more these days because of the fear that people have about ozone and UV is cheaper to setup correctly.
The following articles are the best articles out there regarding ozone in reef tanks
Ozone and the Reef Aquarium, Part 1: Chemistry and Biochemistry by Randy Holmes-Farley - Reefkeeping.com Ozone and the Reef Aquarium, Part 2: Equipment and Safety by Randy Holmes-Farley - Reefkeeping.com Ozone and the Reef Aquarium, Part 3: Changes in a Reef Aquarium upon Initiating Ozone by Randy Holmes-Farley - Reefkeeping.com