"I wanted to welcome you ASAP to our little family here in the States. It's high time we shook hands in person and not just across the sea. I'm pleased as punch about getting to know you all, and I for one will do my level best to sell you on America."

How do you correct this and what is wrong with it.

There is nothing wrong with it, if you are speaking informally. "Pleased as punch" may or may not be understood by foreigners. Consider the audience to whom you will be speaking.

Sra

How do I re-word the sentence?

how much information and what type of communication (email, memo, or letter) is appropriate for each party.

 Write a letter to one party, a memo to one party, and an email to one party. Each communication should be a maximum of 250 words.
 Explain your choice of communication for each party.
 Use appropriate grammar, spelling, style, and format for each type of communication

The given paragraph contains some informal language and a few idiomatic expressions that may not be appropriate in a formal or professional context. To make it more appropriate and clear, you could revise it as follows:

"I would like to extend a warm welcome to you as a new member of our community here in the United States. It is long overdue for us to meet in person, rather than just communicating through distance. I am excited about the opportunity to get to know each and every one of you, and I am fully committed to promoting the positive aspects of America."

In this revised version, the informal language and idiomatic expressions have been replaced with more formal and professional wording.