The salutation shows where the message starts and to whom it is addressed. For letters, "Dear Mr. Smith," is completely conventional for letters. For emails, either that, or, less formally, "Hi, Joe." works well. (Note the period in "Hi, Joe.".).
Valedictions are vexing. A valediction shows where the message ends and by whom it is sent. I have often used "Yours truly, Eric Rasmusen", as being both literally true and clearly convention-driven. But that is somewhat too corny. "Yours faithfully" is too false and pretentious. "Best wishes," "All the best," and "Cheers" all have merit but are often inappropriate.
One valediction I sometimes use is "I.H.S., Eric Rasmusen". For most people, the only meaning of IHS is "Here is where the letters ends", which is fine, since that's the main purpose of a valediction. Others may know its meaning, which I will now explain, and that's fine too.
The meaning of I.H.S. is "In His Service" or "Jesus". Professor Kenneth Elzinga, whom I greatly admire, says he signs his letters writing out the phrase in full, "In His Service". That strikes me as admirable in its Christian witness but too pompous. It makes a claim that the writer hopes is true but seems either overblown or self-aggrandizing: that the writer is trying to act on behalf of God. The Christian is supposed to be doing that always, but if the letter is merely telling someone that the seminar this week is in room CG2069, we smile at this being service to God. It is, but it makes us smile anyway.
I.H.S. has the same meaning, but stated quietly. It has the additional advantage of being a historic Christian code. In Greek, the first three letters of Jesus are Iota, Eta, Sigma, which in Roman letters become I H S. Thus, IHS is a nice nod to God and also identifies the writer's intent to other Christians. At the same time, it offers a witness to non-Christians, in the following way. They see the letters and do not know what they mean. They may then ask the writer or someone else what they mean, and at that point in time they learn, and a useful conversation may start.
IHS does not solve the valediction problem for nonbelievers, but for Christians it may be helpful.
A variant of it is "I hope IHS". That is a pun, meaning either "I hope in His service" or "I hope in Jesus". I like the pun, and I like the greater modesty, since whether I am doing something in God's service is sometimes dubious and since ordinarily what I am doing in the email is entirely mundane (though the Christian is supposed to do *all* things to God's glory, "Soli Deo Gloria", as Bach and Handel wrote on their manuscripts).
Another valediction I've been using, imitating Professor Christopher Connell, is "Shalom, Eric Rasmusen". I like the Hebrew word "shalom", because it is Biblical and encompasses a variety of English words--- completeness, prosperity, peace (think of the Arabic "salaam"). The downside is that it is used as a greeting (and farewell) in modern Hebrew, that many people think it means the same thing as "peace" in English, and that it sounds awkwardly Jewish when used by someone named "Rasmusen". Still another possibility is YT, short for Yours Truly. That has the advantage of being inobtrusive. I like the idea of admitting to people that I am proudly Christian with IHS, but it may too much like boasting. It is best to show one's allegiance to God naturally, without any hint of being forced. I'm still thinking. Comments are welcomed. Email me at [email protected] See also Wikipedia, "Christogram," http://en.wikipedia.org/wiki/Christogram" > http://en.wikipedia.org/wiki/Christogram and "Shalom," http://en.wikipedia.org/wiki/Shalom . This page is at http://rasmusen.org/special/ihs.htm.