Starting on the offense

My strategy is to take as many countries as possible in the first 2 turns. But, then other players approach me, and I cannot defend against them for long. I also get low on money quickly. Am I too aggressive in the beginning, or are my actions from, say, turn 5 on, are bad?

Generally you want to start out aggressively and take the rich and/or populous countries first. Even though you're having money problems, your opponent probably is, too. It depends on how skillful the person you're fighting is.