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First time meetings, especially at a lunch or dinner, usually call for a handwritten note, unless you know the person from an email culture. When in doubt, choose the note. A prompt, sincere, handwritten one is always appropriate and is greatly appreciated by the recipient. It's also good business. Be sure to check spelling and grammar. If your handwriting is illegible, a printed note on your business stationery is fine.An emailed thank-you may be appropriate, depending on the circumstances, the person, and your relationship. Again, defer to the handwritten note if you're in doubt.