what to include in invoice? letter head? emails? as a startup business

Clear concise ways to contact your business.

CompanyName
Contact name
Mailing address
Phone
Email

Contact name is optional, can be included elsewhere in the body or footer of the text

Some people throw a slogan in there or a website address too.

There is no standard, but connecting with your customers is the target of customer communication.

Be creative with it, many companies use a logo on place of their business name.

Be as formal as necessary, but as creative as what works for you and your business.