Unless you're writing a very formal letter, I'd go with the present continuous, 'I'm looking forward to..'. It's more direct and conversational, and tells us how you're feeling at the moment. The present simple, 'I look forward to...', is used as a standard closing formula. It's used just before the sign-off of formal letters, and occasionally at the end of a conversation. Outside these contexts, it can sound rather odd and formal : you would never use it in the middle of a conversation, for example, or in a written correspondence with family or friends. And don't forget that 'look forward to' is followed by a noun or a gerund, never an infinitive. So you'd say, for example, "I'm looking forward to meeting you" ( never 'to meet'). I hope that helps.

Either sounds right to me. I personally use both forms, and I believe they're both correct.

I look forward to (present). I'm looking forward to in (present continuous).