He was, first, much more than a journalist. He was an "organization man." The reason he can be said to have been the most influential conservative of his time is that he catalyzed a lot of practical political activism, often indirectly and behind the scenes, but sometimes more visibly such as hosting the founding of Young Americans for Freedom in 1961. He helped to found, also often directly and sometimes indirectly, important conservative intellectual organizations like the Philadelphia Society.
In other words, his reach was extensive; everyone from the period has a Buckley connection of some kind.
Second was his personality and style. He was the ultimate happy warrior, with an impish smile, flashing eyes, almost always cheerful. More on this in a moment.
He was also slightly exotic, as he spoke with an accent of no known country on the planet. The best I can do is to make it a combination of southern New England patrician leavened with a week at British boarding school. Perhaps it is an effect of having learned English as his second language. As a small child he learned to speak Spanish from his governess before English from his parents.
Despite his aristocratic upbringing and bearing, in his long-running TV show Firing Line, he slouched noticeably in his chair, his hair poorly combed and his suit often visibly wrinkled, often seeming to affect a pose of boredom. In fact he was highly attentive and ready to pounce quickly on any contestable thought from his guest.
Watching Firing Line today, a viewer can't help but be struck by the slow pace compared to Tik-Tok, or 6-minute segments on cable news. Firing Line had a spare set, no moving cameras or colorful, brightly lit backgrounds. It was seemingly designed to make you reach for the remote control to change channels. And yet the show did big ratings for PBS.
Third, a crucial element of his personality and style that deserves separate enumeration was his legendary humor and quick wit. There are countless examples, but two of my favorite examples of his spontaneous wit come from his Playboy magazine interview in 1970. The first question he was asked was, "Why did you agree to sit for an interview with Playboy?" Buckley: "Because I calculate that it is the best way to communicate with my teenage son." Later, asked about solutions to the problem of overpopulation, Buckley shot back: "Get people to stop reading Playboy."