I'm surprised this post has gone unanswered.
You'll be able to catch all sorts of fish while you're in the BWCA. It varies from lake to lake, but panfish, pike, smallies, lake trout & walleyes are all on the menu up there. I'd spend time targetting the smallies and walleyes. If you do that, you're pretty much guaranteed to catch a billion pike.
All you need is a few deep diving crankbaits or some Gulp minnows and a jig. Super easy fishing when it comes to walleyes. I usually like to just run one rod, and have one guy rowing so you just troll your baits along the breaks. Those walleye up there are fairly unpressured compared to the rest of the state.
Bring some oil and Shorelunch with you, because there is no better place for a walleye shore lunch than the BWCA. It's nice to eat some fresh meat while you're in there.
The bass fishing is as good as anywhere in the lower 48. Topwaters are my personal favorite, but spinnerbaits are also hard to beat. I'd bring a little bit of everything, but just remember that you're going to have to portage everything you bring, and weight is a very important consideration. I'd likely just bring two spinning rods and call it good. I am a minimalist when it comes to BWCA trips, so I generally just bring one waterproof plano box full of gear and call it good. Having a bit of bite wire can be beneficial too, since the pike can often make away with a lot of your lures.
Here's the best tip I'm going to offer you: Bring a head net, pants, and a thick long sleeve shirt. Late June is prime time for the hoards of man-eating mosquitos that Minnesota is famous for. Washing your clothes with Permathrin before you trip too can help. Though, keeping bare skin covered is your best bet. As far as bug spray goes, I prefer the lemon eucalyptus types for mosquito deterrent.
What entry point are you using?