Following up after interviews

Thank everyone with whom you met for >15 min! This means graduate students, postdocs, faculty, and administrators.

A simple email should suffice. Following classic thank-you form, it's good to highlight what you particularly enjoyed about the conversation.

If you're thanking a potential adviser, the email should be a bit longer and touch on the research projects that interest you and (if true) the positive interactions you've had with other lab members. If the lab is your first choice, it's okay to say so. You can also gently remind the potential adviser about any outstanding questions he said he'd get back to you on.

If you want to write your letters by hand on your prettiest stationery, that's okay*--as long as they go out immediately. Assuming you have already written a decent note of some kind, the most important thing is that you send it quickly, ideally within 2-3 days of your visit. Snail mail has an obvious disadvantage here. Where I did my PhD, we gave feedback on the candidates several days after the campus visit. It's best if you can beat this deadline.

The whole thanking-people-for-meeting-with-you thing is a generally good habit for life.

*Keep in mind that a lot of researchers travel frequently and don't check their mailboxes that often. I'm one of those people who prefers having all my correspondence in one, easily searchable place (e.g., my gmail inbox, supplemented by tags and threads). Email might make a lot more sense.