Hmm... I don't think there's any specific type you need to use. But what really helped me was leveling up my 6 pokemon to lvl 60 before facing them. Also buy ALOT of revival herbs, max potions, burn heals, paralyze heals etc.
Um, you're Pokemon only really need to be at or a little over lvl.50. Having a Bug-type Pokemon with a Bug-Type move would be perfect, as it would devastate both Caitlyn's Pyschic type Pokemon and Grimsley's Dark types. You'd also be well off having a Rocky type with a decent Rock-type move. Otherwise, just make sure you have a balanced team with a good amounnt of revives and potions.
It's my job to help the next generation, and set a good example for them. And for that I'll gladly lay down my life.
And level 60? Really?
I may not have Black/White, but aren't the regions like, HUGE in those games?
If you're like me, you'd raise them to level 65-70, then beat the crap out of the Elite Four without having to use soo many items.