1 and 3 are correct.
Option 3, using the present continuous, is the more common and natural expression. It tells us what you are feeling at the moment, and is used in spoken and written English.
Option 1, using the present simple, is mainly used as part of a concluding formula in more formal written communications. We don't use this form in spoken English.
Options 2 and 4 are wrong. The verb following 'look forward to' is ALWAYS a gerund (+ing form). It is incorrect to use an infinitive, even though many fluent English speakers who have otherwise perfect grammar make this mistake.
I hope that answers your question.