Yeah, there's a lot of stuff to build around when it comes to gym leaders. Think of them as testing you and your team. If you can't stand up to their tactics and teams, you need to put more polish and honing into what you're doing or go back to the basics.

You can hit them in any order, but classically if you're in Johto, Falkner is first. Pretty awesome dude with a traditional sense to him. Favors birds.

Big thing to watch out for is every gym leader is tight with their teams and experience to back them. You're just some newbie challenger to their seen it all eyes. Don't use your team like they're throwaways, for one that's a crock of shit, and two it's way more effective to have a team that can endure anything thrown at it. Thirdly, they're your bros, pokemon are like dudes who will back you no matter what.

Specialize if you want, you can still win but you got to apply tactics to do it.