Starting traits are a sort of advantage that each leader will get...choose the combination that goes with your game play the best
I personally like playing with Churchill...he is protective and charismatic...so all archers and infantry will get city protection and first strike for free...as well each city gets +1 happiness and 25% less xp needed for upgrades...so I find it is a lot easier with him...although you should choose the best for you.
the wheel is a technology that allows you to build roads...each civ will come with 2 starting technologies, personally the first 2 techs i go for are the wheel and agriculture