Bishop (b4) vs Knight (c3)

I don't know openings well, but this is what I would angle for in this position: continue development, 1.Nf3...Bxc3: 2.dxc3....
You now have a lead in development and the bishop pair. Try to open the position as quickily as possible, open positions are good for the two bishops.
I think your second move should have been Nf3 instead of Knight c3, because it attacks blacks pawn. If he uses the Knight to defend Nc6, then the possibility of pinning his knight may arise.
If white plays, 1e4, 2Nf3 and 3Bb5, this is the begining of the Spannish/Ruy Lopez opening. The lines continue further than that, but it's all the help I can give you :)

2.dxc3-double pawns in this position should not be problem
I suggest you analasye this moves on your chess board at home:
1.Nf3
1.Nd5
1.Qg4
1.Bc4
2.dxc3-double pawns in this position should not be problem
I suggest you analasye this moves on your chess board at home:
1.Nf3
1.Nd5
1.Qg4
1.Bc4
Yes no problem at all, white has resources in this position to do a good game

1 e4 e5 2 Nc3 is a perfectly playable opening. It's called the Vienna Game, and I happen to know two guys rated about 2000-2100 who swear by it. Black's "standard" response is 2...Nf6, but even with this approach white has many good tries at his disposal.
Beginners often learn that doubled pawns are bad, and they are, but they're not so bad that they should be avoided at all costs. Let's say you continue from the position above with 3 Bc4, and then black takes your knight. All black's done is exchange his only developed piece for one of yours.Your doubled pawns may be a minor problem late in the game; but here and now, white still leads in development thanks to the Bc4. Plus, black may regret giving up that bishop later on, when the board starts clearing up and bishops really get strong.
As an alternative, you can play 3 Nf3, attacking black's e5 pawn. If black responds with 3...Nf6, we've reached a position I see very often as black (though I play a different order: 1 e4 e5 2 Nf3 Nf6 3 Nc3 Bb4). White is solid.
In short, don't worry about black's move here. It's not a good move, though it's not a "mistake" you can get an immediate edge from.
Hey, so I'm really only a moderate chess player and have been studying hard to get bettter. I have been running into this position quite often lately and am wondering if there are any articles you know of that debate the principles of this move. The move is basically as follows: My opponent will move his bishop to b4 to attack my knight on c3 (see included simple diagram). I'm wondering what the response should be and pro's and con's of this bishop move.
I know I can use the extra move to get some positional advantages; however, I think having doubled up pawns will hurt my position and black will get a move after my capture anyway. Thanks for any help you can give.