It really depends on what the test participant, or the person paying for the test, wants to learn.
A yDNA (men only) test will give DNA information about a male test participant's paternal line of ancestors. The yDNA is passed from father to sons, father to sons in a relatively unchanged state, except for occasional mutations, from a forefather that lived long before historical family records (that is, long before about 1500 AD). When two yDNA tests match, we know that those two men share a common forefather. Once we know they match, we return to traditional book and record research to try and discover who their common forefather was. In this way we can scientifically prove different branches of a family tree.
Next, every natural born person in the world has 2 genetic parents, 4 grandparents, 16 great-grandparents, 32 great-great-grandparents, 64 great-great-great grandparents, etc. If you take a FamilyFinder test and have a match with a "cousin", you share a common ancestor with your match somewhere in this group of people. There are many surnames in 64 great-great-great grandparents, so the more distant the connections, the harder it is to find the common ancestor for two people. WikiTree makes it a little easier to share these surnames with a cousin-match with the Surname view. Here is my surname view: http://www.wikitree.com/treewidget/Cooper-1/10 Males or females can participate in a FamilyFinder test which I prefer because of their huge database of potential matches. But you could opt for the auDNA test on 23&me.com which includes a genetic medical component if you want that information.
The mtDNA (for men or women) test follows a continuous line of mothers. So that would be your mother, her mother, her mother, and her mother, back through the generations. This is less convenient because we often can't find a mother's maiden name in the tradional book and record research. And in this case, we a talking about a different maiden name in each generation. Personally, I think this is the least informative test for family history research, but it does tell you where your ancient maternal ancestors started long, long ago.
If your contact wishes to order a test kit from FamilyTreeDNA.com, please encourage them to use this link to place your order so that WikiTree gets the referral credit: http://www.familytreedna.com/cj.aspx?ftdna_ref=600
I would be glad to help with any further DNA testing questions. Thanks for the great question.