Almost any dwarf who is idle will become "social". What you want for a mayor is a dwarf with no awkward preferences, so either they won't be issuing mandates (preferably), or at least those they do issue will be easy to fulfill (maybe like barrels, doors or armour, something you'd produce anyway). When they demand "catapult parts" and you're already running short on wood... yeah...
http://dwarffortresswiki.org/index.php/DF2014:Mandate#Mandates_.26_preferences
Keep in mind, nobles can also perform export bans. If a noble bans the export of barrels when the caravans are already leaving with several barrels of prepared food, you'll regret thinking barrels are a great mandate preference. (Doors are pretty safe, though, as you rarely want to trade those away...)
In general, I prefer to make one of my starting seven mayor, and that way I can control who gets picked. Look at your dwarves at embark, and choose a mayor with preferences that you can at least import from the mountainhomes. (Gems are generally the most annoying, so make sure you can import those, but some metals like bismuth or stones like orpiment might also be impossible to find on your embark. Also, look at the wood preferences, and pay attention to whether you're embarking at a place where it will grow, and if not, whether you can trade with the mountainhomes for it.)
You want a mayor that has generally friendly personality traits and likes helping people and isn't vengeful, but isn't necessarily all that honest (you want flatterer and such to help keep dwarves happy).
Give the chosen dwarf a few points of consoler and one point in a couple other social skills to make them the prime choice for expedition leader, and let them go on break slightly more than others. (I make my mayor carpenter, because I usually use carpentry a lot, but there is often time for breaks.)