1 is basically a direct continuation to 0. Many characters that appeared in 0 return in Kiwami so if you can wait 3 months until its released its definitely the best way to go.
So I just played and finished my first Yakuza game with 0. And I love it. And I need to know what happens next. I need another Yakuza game! I have the 4th one on PS+ and I'm itching to start it. Buuut I should probably wait for the remake that's coming out in a few months right? Will they be remaking 2 as well?
4 itself is another great game to play, and since 3 of the characters are brand new in that game you can play it without feeling lost. Its worth noting anyway that Yakuza stories are resolved by the end of each game, some plot points carry across but you won't ever feel lost skipping a game here and there.
Regarding 2 - there is no word on a remake at this point in time apart from a couple of comments from the team that they'd like to have other games in the series "remade" if they had the time/opportunity. A new Yakuza game is in development, and more details will be released at the end of this month (I can't wait!) but it sounds more like they are gearing up for a brand new chapter in the series, rather than a remake.