There is no the “best”.
Jatco is the largest, they make several different transmission types, but much of their volume is devoted to CVTs for Nissan cars. They are majority owned by Nissan, and supply Mitsubishi and Suzuki as well, and have supplied Chrysler/Jeep/FCA for a number of years. They have the most market share of any manufacturer, and mostly focus on CVTs these days. Depending on which one of their press releases you read, they make anywhere from 30–50% of all the CVTs sold in cars in the world.
Don Sutton referred to Aisin, which makes a few different models that are focused mostly on moderate torque gas engines, as well as the entire CVT kit for things like the Prius and other companies hybrids. Aisin is partially owned by Toyota.
Honda makes their own, and they are unusual in this respect. I suspect, but do not know for sure, that Honda will move their CVT to their smallest cars at some point, as they have widely publicized their coming 11 speed dual clutch autoshifter.
These are the major manufacturers of CVTs, as they are not widely used outside of the Japanese industry. Most of the German companies are no longer focusing on CVTs, but rather focusing on more multi speed dual clutch autoshifters.
The CVT equipped cars in tiny cars have done fairly well, as they have in Hybrids. But in mid size cars and up, they haven’t really succeeded as widely as in the smaller city cars and hybrids.
If I had to handicap the most mature CVTs made by one company, I’d have to say Jatco, and probably Aisin next. Jatco has the broadest lineup and the most units deployed, which means they have the most field experience and therefore, likely the best reliability over the long term. Aisin also has made plenty, but their most successful transmissions are focused on Hybrids, especially the Prius.