The “go-to” Flash (that is, the person the majority of comic readers think of when referring to a character) has changed over the decades. Of course, Jar Garrick was the original Flash of the first continuity, retroactively named Earth-Two, which took place in what we call the Golden Age. In the mid-1950s, DC transitioned into its Silver Age, which was set in a new continuity, called Earth-One. In this universe, Barry Allen was the first to be called the Flash. Barry and Jay worked together a few times, but Barry became the household (comic-loving household, that is) name for the Flash moniker. During Crisis on Infinite Earths, the event that merged the universes in the multiverse into a singular earth called New Earth, Barry Allen sacrificed himself, as his former protégé Wally West, who had been Kid Flash until he quit heroics shortly before this event, adopted the title of Flash. Wally was 19 years old and turned 20 shortly afterward. Over the next two-nearly-three decades, Wally West was the Flash. Sure, a few years in, Jar Garrick (who had been folded into New Earth continuity) reappeared, but Jay was semi-retired and publicly declared Wally the main bearer of the Flash mantle.
Wally became fully ingrained into the adult heroic community, and he was the first protégé to be fully accepted as the new bearer of one of the adult monikers. His memberships in six to seven incarnations of the Justice League helped him gain a strong standing, as did his progression into discovering new ways to use the Speed Force—which neither Wally, Barry, nor Jay knew about before Wally’s adulthood as Flash. Wally grew into his mid-20s as Flash and had a family and such. New Earth was the time period during which the most new readers and most avid readers came into the picture, so for all those many readers, Wally West was their Flash. Barry Allen was around during a time of publication where stories were episodic and everything was slightly goofy. He had a cookie-cutter heroic personality, and many people both readers and in-universe characters and friends of Barry alike found him a bit boring. Wally had the most personality and had the largest character-growth arcs, which people enjoyed. Bart Allen was only the Flash for a year, so he was never really the “main” Flash of an era, as Wally returned to the mantle.
Anyhow, by the time Barry Allen was brought back in the late 2000s, shortly before Flashpoint, Wally was still the majority of people’s personal go-to Flash. Barry was the lead character of Flashpoint, which led to the new mainstream continuity, Prime Earth. For Prime Earth, DC pushed for the “classic” heroes to be front-and-center and to be rebooted for the most part. Thus, Barry Allen was made to be the one and only Flash in that universe for the first several years. A version of Wally West, the teenage one we now call Wallace, appeared, but fans didn’t like him at first. He was created to be PE’s version of Wally West, but he was so drastically different that fans of Wally, who again I remind you had been the Flash for so long, felt like DC was slapping them in the face. DC responded by bringing the classic ginger Wally West back into Prime Earth and simply making him cousins with the younger one. Wally West was a Flash again, but this time he took a backseat, unlike when Jay returned last time and took a backseat for Wally. Barry had become the Flash for DC again, largely due to the popularity the character gained from the CW television series and the subsequent JL movie universe. So, for comic readers who just became fans this last decade, Barry Allen is the person they think of when they think of Flash. Part of the insult came from the fact that DC took many of Wally’s character traits and pasted them on PE Barry. So, all the things that people like about Barry’s personality now came from Wally. I can imagine how Wally fans find that unfair. I’ve read all of Wally’s 250+ Flash series after all, so I understand. In any event, the “go-to” Flash tends to depend on who has led the most titles for the longest stretch of time per era, as well as who has been the most represented in non-comic media.
Oh, and Max Mercury is the speedster who most adopts the role of the wise and older sage hero. He served as a mentor to Jay Garrick, Johnny Quick, Wally West and Bart Allen.