I could use some help.  We want to go to the BWCA for 4-5 days.  4 of us(mom, dad, 20 and 18 year old), we want to fish and be away from a ton of people.  My daughter doesn't love physical exertion.  Not worried about paddling as much as the portages.

Any suggestions of where to go and what outfitter to use to get canoes?    I would love advice as well, do we do a four-person or 2, two-person canoes?

Bill had good advice. I'll just add my two cents.

If you are wanting to fish, I would use two tandem canoes instead of a 4-person. I have used 3-person canoes often, never a 4-person. However, the disadvantages will probably be magnified even more.

The biggest advantage is everyone is together, and those things can move when everyone is paddling. Also would give your daughter a bit of a break - not as important that she paddles. In a tandem canoe, she has to paddle. 

Disadvantages:

• Space - even though the canoes are bigger, space is at a premium. The Wenonah MN 4 is 23 feet long, but you have to fit four people and all of their gear. Other brands are not as long as Wenonah's, and things are tighter.
• If you are using a really long canoe, "parking" the canoe at campsites and portages is a pain. 
• Fishing is very difficult. When I am in a 3-person canoe, I generally opt to steer the canoe and let the other two people fish. If I am trying to fish, having three lines in the water is too much to worry about. I can't imagine trying to do it with 4 people. I have no problem fishing and paddling in a tandem canoe. 

Typically the farther you travel, the fewer people you see. Long portages usually equals a measure of solitude. Without either of those, it is more difficult. However, you can find solitude in other ways. One suggestion is finding an "out-of-the-way" campsite on a busy lake. My wife and I spent a July 4th weekend on a busy lake and did not see anybody - our campsite was in a remote bay off of the main travel route. Another suggestion is to snag a permit (if possible) that does not allow a lot of visitors. These are usually small areas with few campsites, so they cannot allow a lot of people in. However, these areas are also limited in "exploring potential." 

Little Indian Sioux River South to Bootleg Lake is an example of a "few permits" entry point. There are a couple of short portages, but it is mostly paddling. There is one permit every other day, so not easy to get.  Fishing was excellent the time I went. The first couple of days it was a fish every cast. Then the cold front came through and stopped the fishing. There are only two campsites on the lake. It can be a problem to get one of them with very few options if they are both taken, but if you are willing to take the risk... On our trip, we were the only ones on the lake for a day. The other campsite was taken the next day, but we didn't really see them at all. The last night we were there, someone came to the lake from the south, and there were no campsites. We let them stay in our campsite for the night. No place to explore since it is only that one lake, but it is easy paddling the river and only a couple of short portages.

If you can let us know more about your priorities, you will get more/better suggestions.