It really all depends on your tolerance for terrible combat and long load times. The first Yakuza had some of the worst load times on the PS2, and since the game uses random encounters, this is a huge problem. The combat also feels very unsatisfying as you'll be hitting air most of the time as the lock-on system is completely broken (maybe it was never meant to be a lock-on system and was instead a strafing system -- I dunno...). All of this was fixed in Yakuza 2, however, which is my favorite out of the first 3 numbered games.
Not sure why so many people suggest you play them in order though as the stories are all pretty self-contained, and if you absolutely must know what happened in the previous games, there's the recap trailer feature as others have mentioned.
Anyway, regardless of where you decide to start, here's a few tips for the entire series:
In the first game, make sure to get a Kevlar Vest as soon as possible (just look it up in a guide) to protect yourself from being knocked down by bullets, otherwise you're gonna have a very hard time with one of the bosses. I managed to take him down on first try, but I only had one hit left on my health bar and had used up all my energy drinks. You don't have to worry about it in subsequent games though as bullets don't have the ability to knock you down anymore.
Never play a Yakuza game on Hard Mode. It makes the combat a complete chore as enemies will be turtling all the time and have significantly increased health bars. It doesn't actually increase the difficulty of the game, however, as you can just fill your entire inventory with energy drinks and power through anything the game throws at you.
Whenever starting a new Yakuza game, I suggest checking a guide to see where all the move tutors are. I always seem to miss these and then don't unlock the coolest moves until the very end of the game.
And finally, if you do decide start at the very beginning of the series, make sure to space them out a bit as they're all very, very similar.